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lizlozada

  • 3 years ago

Use the chain rule to find the derivative of (2x-7)^3.

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  1. myininaya
    • 3 years ago
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    So the chain rule is: |dw:1348707512136:dw|

  2. myininaya
    • 3 years ago
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    f(x) is the outside function g(x) is the inside function

  3. mathslover
    • 3 years ago
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    Should I interrupt?

  4. myininaya
    • 3 years ago
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    Which function in this problem is f(x)?

  5. myininaya
    • 3 years ago
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    Which function in this problem is g(x)?

  6. lizlozada
    • 3 years ago
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    the power of 3 is the outside function, or f(x) and 2x-7 is the inside function or g(x)

  7. myininaya
    • 3 years ago
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    So f(x)=x^3 and g(x)=2x-7 correct :)

  8. mathslover
    • 3 years ago
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    how ?

  9. myininaya
    • 3 years ago
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    f is the outside function g is the inside 2x-7 is inside the ( )^3

  10. myininaya
    • 3 years ago
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    g is inside f

  11. myininaya
    • 3 years ago
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    so g is 2x-7 f is x^3

  12. myininaya
    • 3 years ago
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    \[f(g(x))=f(2x-7)=(2x-7)^3 \text{ since } f(x)=x^3 \text{ and } g(x)=2x-7\]

  13. myininaya
    • 3 years ago
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    Now if you want just plug into the formula above that I gave you

  14. lizlozada
    • 3 years ago
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    ok so you would set it up x^3(2x-7)^2?

  15. myininaya
    • 3 years ago
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    The formula known as the chain rule.

  16. myininaya
    • 3 years ago
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    If g(x)=2x-7, then g'(x)= If f(x)=x^3, then f'(x)=?

  17. lizlozada
    • 3 years ago
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    ohhh 3x^2

  18. myininaya
    • 3 years ago
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    And (2x-7)'=?

  19. lizlozada
    • 3 years ago
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    2

  20. myininaya
    • 3 years ago
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    \[(f(g(x))'=f'(g(x))\cdot g'(x)=f'(2x-7) \cdot 2\]

  21. myininaya
    • 3 years ago
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    Now to find f'(2x-7) you need to plug 2x-7 into f'

  22. mathslover
    • 3 years ago
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    is this the same : f(g(x)) = f(x) g(x)

  23. mathslover
    • 3 years ago
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    OK i am interrupting the solution, will take time from @myininaya mam to teach me this,

  24. myininaya
    • 3 years ago
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    f(g(x)) means f composed with g

  25. myininaya
    • 3 years ago
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    It is not multiplication

  26. lizlozada
    • 3 years ago
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    would it be 3x^2(2x-7)x2?

  27. myininaya
    • 3 years ago
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    No not exactly

  28. lizlozada
    • 3 years ago
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    does the 2x-7 have an exponent?

  29. myininaya
    • 3 years ago
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    f'(x)=3x^2 f'(2x-7)= <---to find this one replace x with 2x-7

  30. lizlozada
    • 3 years ago
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    why?

  31. myininaya
    • 3 years ago
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    the new input is 2x-7

  32. myininaya
    • 3 years ago
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    all the outputs have this form 3x^2

  33. myininaya
    • 3 years ago
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    except x is the input

  34. myininaya
    • 3 years ago
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    and for f'(2x-7), the new input is 2x-7

  35. lizlozada
    • 3 years ago
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    i don't understand...

  36. Shironlom
    • 3 years ago
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    |dw:1348708652193:dw|

  37. Shironlom
    • 3 years ago
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    Tip: Try to sense the pattern in order to absorb the chain rule formula if you're looking for them online

  38. lizlozada
    • 3 years ago
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    ok so 3(2x-7)^2 x 2?

  39. lizlozada
    • 3 years ago
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    @Shironlom ?

  40. cgreenwade2000
    • 3 years ago
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    Yes.

  41. lizlozada
    • 3 years ago
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    thank you!

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