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#differentiation — Public Fediverse posts

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  1. Alright, future engineers!
    **The Derivative:** Measures a function's instantaneous rate of change at any point.
    Ex: Power Rule `d/dx(x^n) = n*x^(n-1)`
    Pro-Tip: Always think of it as the *slope of the tangent line*! It makes applications like optimization crystal clear.
    #Calculus #Differentiation #STEM #StudyNotes

  2. Alright, future engineers!
    **Product Rule:** Differentiates the product of two functions.
    Formula: `(uv)' = u'v + uv'`
    Pro-Tip: It's NOT just `u'v'`! Each function gets a turn being differentiated while the other stays put.

    #Calculus #Differentiation #STEM #StudyNotes

  3. Alright, future engineers!
    **Product Rule:** Differentiates the product of two functions.
    Formula: `(uv)' = u'v + uv'`
    Pro-Tip: It's NOT just `u'v'`! Each function gets a turn being differentiated while the other stays put.

    #Calculus #Differentiation #STEM #StudyNotes

  4. Alright, future engineers!
    **Chain Rule:** Differentiates composite functions (function within a function).
    Ex: `d/dx sin(x^2) = cos(x^2) * 2x`.
    Pro-Tip: Always differentiate outside in!
    #Calculus #Differentiation #STEM #StudyNotes

  5. Alright, future engineers!
    **Chain Rule:** Differentiates composite functions (function within a function).
    Ex: `d/dx sin(x^2) = cos(x^2) * 2x`.
    Pro-Tip: Always differentiate outside in!
    #Calculus #Differentiation #STEM #StudyNotes

  6. #differentiation : the action of distinguishing between things

    - French: différenciation

    - German: die Unterscheidung

    - Italian: differenziazione

    - Portuguese: diferenciação

    - Spanish: diferencia

    ------------

    Guess the next word of the hour @ 24hippos.com

  7. #differentiation : the action of distinguishing between things

    - French: différenciation

    - German: die Unterscheidung

    - Italian: differenziazione

    - Portuguese: diferenciação

    - Spanish: diferencia

    ------------

    Guess the next word of the hour @ 24hippos.com

  8. #differentiation : the action of distinguishing between things

    - French: différenciation

    - German: die Unterscheidung

    - Italian: differenziazione

    - Portuguese: diferenciação

    - Spanish: diferencia

    ------------

    Guess the next word of the hour @ 24hippos.com

  9. #differentiation : the action of distinguishing between things

    - French: différenciation

    - German: die Unterscheidung

    - Italian: differenziazione

    - Portuguese: diferenciação

    - Spanish: diferencia

    ------------

    Guess the next word of the hour @ 24hippos.com

  10. #differentiation : the action of distinguishing between things

    - French: différenciation

    - German: die Unterscheidung

    - Italian: differenziazione

    - Portuguese: diferenciação

    - Spanish: diferencia

    ------------

    Guess the next word of the hour @ 24hippos.com

  11. Alright, future engineers!
    The **Chain Rule** differentiates a function inside another (a composite function).
    Ex: `d/dx f(g(x)) = f'(g(x)) * g'(x)`
    Pro-Tip: Differentiate the *outside*, then multiply by the derivative of the *inside*! Think 'onion layers.'
    #Calculus #Differentiation #STEM #StudyNotes

  12. Alright, future engineers!
    The **Chain Rule** differentiates a function inside another (a composite function).
    Ex: `d/dx f(g(x)) = f'(g(x)) * g'(x)`
    Pro-Tip: Differentiate the *outside*, then multiply by the derivative of the *inside*! Think 'onion layers.'
    #Calculus #Differentiation #STEM #StudyNotes

  13. Alright, future engineers!

    The **Product Rule** differentiates a product of two functions.
    Formula: `(fg)' = f'g + fg'`
    Pro-Tip: 'First D Second + Second D First' is a classic mnemonic!

    #Calculus #Differentiation #STEM #StudyNotes

  14. Alright, future engineers!

    The **Product Rule** differentiates a product of two functions.
    Formula: `(fg)' = f'g + fg'`
    Pro-Tip: 'First D Second + Second D First' is a classic mnemonic!

    #Calculus #Differentiation #STEM #StudyNotes

  15. Alright, future engineers!

    The **Product Rule** differentiates a product of two functions.
    Formula: `(fg)' = f'g + fg'`
    Pro-Tip: 'First D Second + Second D First' is a classic mnemonic!

    #Calculus #Differentiation #STEM #StudyNotes

  16. Alright, future engineers!

    The **Product Rule** differentiates a product of two functions.
    Formula: `(fg)' = f'g + fg'`
    Pro-Tip: 'First D Second + Second D First' is a classic mnemonic!

    #Calculus #Differentiation #STEM #StudyNotes

  17. Alright, future engineers!

    The **Product Rule** differentiates a product of two functions.
    Formula: `(fg)' = f'g + fg'`
    Pro-Tip: 'First D Second + Second D First' is a classic mnemonic!

    #Calculus #Differentiation #STEM #StudyNotes

  18. Chain Rule helps differentiate composite functions (function of a function). Formula: d/dx [f(g(x))] = f'(g(x)) * g'(x). Ex: d/dx [(x^2+1)^3] = 3(x^2+1)^2 * (2x). Pro-Tip: Always think Outside-Inside! Differentiate the outer function first, then multiply by the inner's derivative.
    #Calculus #Differentiation #STEM #StudyNotes

  19. Chain Rule helps differentiate composite functions (function of a function). Formula: d/dx [f(g(x))] = f'(g(x)) * g'(x). Ex: d/dx [(x^2+1)^3] = 3(x^2+1)^2 * (2x). Pro-Tip: Always think Outside-Inside! Differentiate the outer function first, then multiply by the inner's derivative.
    #Calculus #Differentiation #STEM #StudyNotes

  20. Chain Rule helps differentiate composite functions (function of a function). Formula: d/dx [f(g(x))] = f'(g(x)) * g'(x). Ex: d/dx [(x^2+1)^3] = 3(x^2+1)^2 * (2x). Pro-Tip: Always think Outside-Inside! Differentiate the outer function first, then multiply by the inner's derivative.
    #Calculus #Differentiation #STEM #StudyNotes

  21. Chain Rule helps differentiate composite functions (function of a function). Formula: d/dx [f(g(x))] = f'(g(x)) * g'(x). Ex: d/dx [(x^2+1)^3] = 3(x^2+1)^2 * (2x). Pro-Tip: Always think Outside-Inside! Differentiate the outer function first, then multiply by the inner's derivative.
    #Calculus #Differentiation #STEM #StudyNotes

  22. Chain Rule helps differentiate composite functions (function of a function). Formula: d/dx [f(g(x))] = f'(g(x)) * g'(x). Ex: d/dx [(x^2+1)^3] = 3(x^2+1)^2 * (2x). Pro-Tip: Always think Outside-Inside! Differentiate the outer function first, then multiply by the inner's derivative.
    #Calculus #Differentiation #STEM #StudyNotes

  23. #differentiation : the act of distinguishing or describing a thing, by giving its different, or specific difference

    - French: différenciation

    - German: die Unterscheidung

    - Italian: differenziazione

    - Portuguese: diferenciação

    - Spanish: diferencia

    ------------

    Guess the next word of the hour @ 24hippos.com

  24. #differentiation : the act of distinguishing or describing a thing, by giving its different, or specific difference

    - French: différenciation

    - German: die Unterscheidung

    - Italian: differenziazione

    - Portuguese: diferenciação

    - Spanish: diferencia

    ------------

    Guess the next word of the hour @ 24hippos.com

  25. #differentiation : the act of distinguishing or describing a thing, by giving its different, or specific difference

    - French: différenciation

    - German: die Unterscheidung

    - Italian: differenziazione

    - Portuguese: diferenciação

    - Spanish: diferencia

    ------------

    Guess the next word of the hour @ 24hippos.com

  26. #differentiation : the act of distinguishing or describing a thing, by giving its different, or specific difference

    - French: différenciation

    - German: die Unterscheidung

    - Italian: differenziazione

    - Portuguese: diferenciação

    - Spanish: diferencia

    ------------

    Guess the next word of the hour @ 24hippos.com

  27. #differentiation : the act of distinguishing or describing a thing, by giving its different, or specific difference

    - French: différenciation

    - German: die Unterscheidung

    - Italian: differenziazione

    - Portuguese: diferenciação

    - Spanish: diferencia

    ------------

    Guess the next word of the hour @ 24hippos.com

  28. "Always remember that conformity is where tomorrow's greatness goes to die." - Futurist Jim Carroll

    ----

    Futurist Jim Carroll is writing his end-of-2025 / introduction-to-2026 series, 26 Principles for 2026. You can follow along at 2026.jimcarroll.com. He welcomes your comments.
    ---

    I've long suggested that one of the best ways to align with the future is through this thinking: when everybody is running one way, run the other way!

    Be the contrarian. The hole in the bucket, the square peg with a bunch of round holes, the one who says "why not?' when everyone else is saying 'why?'

    We are on Day 17. Yesterday, we looked at the terrifying math of the future—the sheer scale of change that is coming. 1-2-4-16-64 vs. 1-2-3-45.

    When faced with that kind of overwhelming scale, the natural human instinct is to feel overwhelmed. And I am willing to admit that one reaction I see in common with all of my audiences is that this feeling is universal. I've been doing text-message-based polling from the stage for over 15 years, and one overwhelmingly consistent attitude is that people feel universally overwhelmed by the speed of the future.

    So they try to avoid it. They try to fit in. They take the cautious route.

    They choose the comfortable over discomfort.

    The result? When we feel a need for comfort, to fit in, to follow the herd instinct, we try to be like everyone else. We look for safety in numbers. Case in point: we look at our competitors and say, "Well, they are doing AI this way, so we should too." Korn Ferry made this observation about AI: "Among the most expensive keeping-up-with-the-Joneses games in corporate history."

    Need more proof? We seek out "best practices," which is usually just a fancy word for "copying the average."

    I rest my case.

    In a linear world, fitting in was a survival strategy. You survived by being a cog that fit perfectly into the machine.

    In an exponential world, conformity is a death sentence.

    Here's why: read the full post at the link below.

    ----

    **#Uniqueness** **#Conformity** **#Contrarian** **#Rebellion** **#Innovation** **#Curiosity** **#Differentiation** **#Misfits** **#Authenticity** **#Exponential**

    The story of Oblio has defined much of Futurist Jim Carroll’s approach to life.

    Original post: jimcarroll.com/2025/12/decodin

  29. "Always remember that conformity is where tomorrow's greatness goes to die." - Futurist Jim Carroll

    ----

    Futurist Jim Carroll is writing his end-of-2025 / introduction-to-2026 series, 26 Principles for 2026. You can follow along at 2026.jimcarroll.com. He welcomes your comments.
    ---

    I've long suggested that one of the best ways to align with the future is through this thinking: when everybody is running one way, run the other way!

    Be the contrarian. The hole in the bucket, the square peg with a bunch of round holes, the one who says "why not?' when everyone else is saying 'why?'

    We are on Day 17. Yesterday, we looked at the terrifying math of the future—the sheer scale of change that is coming. 1-2-4-16-64 vs. 1-2-3-45.

    When faced with that kind of overwhelming scale, the natural human instinct is to feel overwhelmed. And I am willing to admit that one reaction I see in common with all of my audiences is that this feeling is universal. I've been doing text-message-based polling from the stage for over 15 years, and one overwhelmingly consistent attitude is that people feel universally overwhelmed by the speed of the future.

    So they try to avoid it. They try to fit in. They take the cautious route.

    They choose the comfortable over discomfort.

    The result? When we feel a need for comfort, to fit in, to follow the herd instinct, we try to be like everyone else. We look for safety in numbers. Case in point: we look at our competitors and say, "Well, they are doing AI this way, so we should too." Korn Ferry made this observation about AI: "Among the most expensive keeping-up-with-the-Joneses games in corporate history."

    Need more proof? We seek out "best practices," which is usually just a fancy word for "copying the average."

    I rest my case.

    In a linear world, fitting in was a survival strategy. You survived by being a cog that fit perfectly into the machine.

    In an exponential world, conformity is a death sentence.

    Here's why: read the full post at the link below.

    ----

    **#Uniqueness** **#Conformity** **#Contrarian** **#Rebellion** **#Innovation** **#Curiosity** **#Differentiation** **#Misfits** **#Authenticity** **#Exponential**

    The story of Oblio has defined much of Futurist Jim Carroll’s approach to life.

    Original post: jimcarroll.com/2025/12/decodin

  30. "Always remember that conformity is where tomorrow's greatness goes to die." - Futurist Jim Carroll

    ----

    Futurist Jim Carroll is writing his end-of-2025 / introduction-to-2026 series, 26 Principles for 2026. You can follow along at 2026.jimcarroll.com. He welcomes your comments.
    ---

    I've long suggested that one of the best ways to align with the future is through this thinking: when everybody is running one way, run the other way!

    Be the contrarian. The hole in the bucket, the square peg with a bunch of round holes, the one who says "why not?' when everyone else is saying 'why?'

    We are on Day 17. Yesterday, we looked at the terrifying math of the future—the sheer scale of change that is coming. 1-2-4-16-64 vs. 1-2-3-45.

    When faced with that kind of overwhelming scale, the natural human instinct is to feel overwhelmed. And I am willing to admit that one reaction I see in common with all of my audiences is that this feeling is universal. I've been doing text-message-based polling from the stage for over 15 years, and one overwhelmingly consistent attitude is that people feel universally overwhelmed by the speed of the future.

    So they try to avoid it. They try to fit in. They take the cautious route.

    They choose the comfortable over discomfort.

    The result? When we feel a need for comfort, to fit in, to follow the herd instinct, we try to be like everyone else. We look for safety in numbers. Case in point: we look at our competitors and say, "Well, they are doing AI this way, so we should too." Korn Ferry made this observation about AI: "Among the most expensive keeping-up-with-the-Joneses games in corporate history."

    Need more proof? We seek out "best practices," which is usually just a fancy word for "copying the average."

    I rest my case.

    In a linear world, fitting in was a survival strategy. You survived by being a cog that fit perfectly into the machine.

    In an exponential world, conformity is a death sentence.

    Here's why: read the full post at the link below.

    ----

    **#Uniqueness** **#Conformity** **#Contrarian** **#Rebellion** **#Innovation** **#Curiosity** **#Differentiation** **#Misfits** **#Authenticity** **#Exponential**

    The story of Oblio has defined much of Futurist Jim Carroll’s approach to life.

    Original post: jimcarroll.com/2025/12/decodin

  31. "Always remember that conformity is where tomorrow's greatness goes to die." - Futurist Jim Carroll

    ----

    Futurist Jim Carroll is writing his end-of-2025 / introduction-to-2026 series, 26 Principles for 2026. You can follow along at 2026.jimcarroll.com. He welcomes your comments.
    ---

    I've long suggested that one of the best ways to align with the future is through this thinking: when everybody is running one way, run the other way!

    Be the contrarian. The hole in the bucket, the square peg with a bunch of round holes, the one who says "why not?' when everyone else is saying 'why?'

    We are on Day 17. Yesterday, we looked at the terrifying math of the future—the sheer scale of change that is coming. 1-2-4-16-64 vs. 1-2-3-45.

    When faced with that kind of overwhelming scale, the natural human instinct is to feel overwhelmed. And I am willing to admit that one reaction I see in common with all of my audiences is that this feeling is universal. I've been doing text-message-based polling from the stage for over 15 years, and one overwhelmingly consistent attitude is that people feel universally overwhelmed by the speed of the future.

    So they try to avoid it. They try to fit in. They take the cautious route.

    They choose the comfortable over discomfort.

    The result? When we feel a need for comfort, to fit in, to follow the herd instinct, we try to be like everyone else. We look for safety in numbers. Case in point: we look at our competitors and say, "Well, they are doing AI this way, so we should too." Korn Ferry made this observation about AI: "Among the most expensive keeping-up-with-the-Joneses games in corporate history."

    Need more proof? We seek out "best practices," which is usually just a fancy word for "copying the average."

    I rest my case.

    In a linear world, fitting in was a survival strategy. You survived by being a cog that fit perfectly into the machine.

    In an exponential world, conformity is a death sentence.

    Here's why: read the full post at the link below.

    ----

    **#Uniqueness** **#Conformity** **#Contrarian** **#Rebellion** **#Innovation** **#Curiosity** **#Differentiation** **#Misfits** **#Authenticity** **#Exponential**

    The story of Oblio has defined much of Futurist Jim Carroll’s approach to life.

    Original post: jimcarroll.com/2025/12/decodin

  32. "Always remember that conformity is where tomorrow's greatness goes to die." - Futurist Jim Carroll

    ----

    Futurist Jim Carroll is writing his end-of-2025 / introduction-to-2026 series, 26 Principles for 2026. You can follow along at 2026.jimcarroll.com. He welcomes your comments.
    ---

    I've long suggested that one of the best ways to align with the future is through this thinking: when everybody is running one way, run the other way!

    Be the contrarian. The hole in the bucket, the square peg with a bunch of round holes, the one who says "why not?' when everyone else is saying 'why?'

    We are on Day 17. Yesterday, we looked at the terrifying math of the future—the sheer scale of change that is coming. 1-2-4-16-64 vs. 1-2-3-45.

    When faced with that kind of overwhelming scale, the natural human instinct is to feel overwhelmed. And I am willing to admit that one reaction I see in common with all of my audiences is that this feeling is universal. I've been doing text-message-based polling from the stage for over 15 years, and one overwhelmingly consistent attitude is that people feel universally overwhelmed by the speed of the future.

    So they try to avoid it. They try to fit in. They take the cautious route.

    They choose the comfortable over discomfort.

    The result? When we feel a need for comfort, to fit in, to follow the herd instinct, we try to be like everyone else. We look for safety in numbers. Case in point: we look at our competitors and say, "Well, they are doing AI this way, so we should too." Korn Ferry made this observation about AI: "Among the most expensive keeping-up-with-the-Joneses games in corporate history."

    Need more proof? We seek out "best practices," which is usually just a fancy word for "copying the average."

    I rest my case.

    In a linear world, fitting in was a survival strategy. You survived by being a cog that fit perfectly into the machine.

    In an exponential world, conformity is a death sentence.

    Here's why: read the full post at the link below.

    ----

    **#Uniqueness** **#Conformity** **#Contrarian** **#Rebellion** **#Innovation** **#Curiosity** **#Differentiation** **#Misfits** **#Authenticity** **#Exponential**

    The story of Oblio has defined much of Futurist Jim Carroll’s approach to life.

    Original post: jimcarroll.com/2025/12/decodin

  33. #differentiation : the act of distinguishing or describing a thing, by giving its different, or specific difference

    - French: différenciation

    - German: die Unterscheidung

    - Italian: differenziazione

    - Portuguese: diferenciação

    - Spanish: diferencia

    ------------

    Join our new Discord Server for language learners @ wordofthehour.org/discord

  34. #differentiation : the act of distinguishing or describing a thing, by giving its different, or specific difference

    - French: différenciation

    - German: die Unterscheidung

    - Italian: differenziazione

    - Portuguese: diferenciação

    - Spanish: diferencia

    ------------

    Join our new Discord Server for language learners @ wordofthehour.org/discord

  35. #differentiation : the act of distinguishing or describing a thing, by giving its different, or specific difference

    - French: différenciation

    - German: die Unterscheidung

    - Italian: differenziazione

    - Portuguese: diferenciação

    - Spanish: diferencia

    ------------

    Join our new Discord Server for language learners @ wordofthehour.org/discord

  36. #differentiation : the act of distinguishing or describing a thing, by giving its different, or specific difference

    - French: différenciation

    - German: die Unterscheidung

    - Italian: differenziazione

    - Portuguese: diferenciação

    - Spanish: diferencia

    ------------

    Join our new Discord Server for language learners @ wordofthehour.org/discord

  37. Oh, the irony! 🚨 The article about #differentiation goes on a tangent and differentiates itself into oblivion. Maybe they should try finding the derivative of their server errors before tackling complex math! 🤦‍♂️
    stochasticlifestyle.com/the-nu #irony #servererrors #mathhumor #tangentialthinking #HackerNews #ngated

  38. #USA #K12 #education #LLM question:

    #Teachers can now create differentiated materials for #EnglishLearners or students with IEPs quickly and easily. This was not true in the past, so although #differentiation has been a best practice for many years, I suspect most teachers didn't have time to do it. Now though, many can do it.

    So, what about the #pedagogy? How do teachers use these materials with the #students? Prolly, teachers have more experience with them in last 2 years than in prev. 20.

  39. #USA #K12 #education #LLM question:

    #Teachers can now create differentiated materials for #EnglishLearners or students with IEPs quickly and easily. This was not true in the past, so although #differentiation has been a best practice for many years, I suspect most teachers didn't have time to do it. Now though, many can do it.

    So, what about the #pedagogy? How do teachers use these materials with the #students? Prolly, teachers have more experience with them in last 2 years than in prev. 20.

  40. #USA #K12 #education #LLM question:

    #Teachers can now create differentiated materials for #EnglishLearners or students with IEPs quickly and easily. This was not true in the past, so although #differentiation has been a best practice for many years, I suspect most teachers didn't have time to do it. Now though, many can do it.

    So, what about the #pedagogy? How do teachers use these materials with the #students? Prolly, teachers have more experience with them in last 2 years than in prev. 20.

  41. #USA #K12 #education #LLM question:

    #Teachers can now create differentiated materials for #EnglishLearners or students with IEPs quickly and easily. This was not true in the past, so although #differentiation has been a best practice for many years, I suspect most teachers didn't have time to do it. Now though, many can do it.

    So, what about the #pedagogy? How do teachers use these materials with the #students? Prolly, teachers have more experience with them in last 2 years than in prev. 20.

  42. #USA #K12 #education #LLM question:

    #Teachers can now create differentiated materials for #EnglishLearners or students with IEPs quickly and easily. This was not true in the past, so although #differentiation has been a best practice for many years, I suspect most teachers didn't have time to do it. Now though, many can do it.

    So, what about the #pedagogy? How do teachers use these materials with the #students? Prolly, teachers have more experience with them in last 2 years than in prev. 20.

  43. AI Applications Expand Globally: 2025 Insight Report on Infrastructure, Market Readiness, and Scenario-based Differentiation Industry White Paper

    Abstract: GPU Cloud Strengthens the Computing Infrastructure, Powering the Global Expansion of AI Appli…
    #NewsBeep #News #Computing #2025 #AI #and #Applications #AU #Australia #Differentiation #Expand #globally #industry #infrastructure #Insight #market #on #Paper #Readiness #Report #Scenario-based #Technology #White
    newsbeep.com/au/60558/