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Math Help - Derivative of Composition of Functions Question

  1. #1
    Junior Member StarlitxSunshine's Avatar
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    Derivative of Composition of Functions Question

    Heylo <3

    I have the answer to the question, but I can't seem to quite get to it successfully.

    Please & thank you =)

    Let f(x)= x^5 and g(x)= 2x-3, Find (g o f)(x) and (g o f)'x

    -Finding (g o f)(x) -->
    f(x) = x^5
    g(x^5)= 2x^5-3
    Which is the correct answer for part 1

    -Finding (g o f)'(x) -->
    g'(f(x))(f'(x))
    g'(x^5)(5x^4)
    10x^4 * 5x^4
    = 50x^8
    But the answer 10x^4
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  2. #2
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    Quote Originally Posted by StarlitxSunshine View Post
    Heylo <3

    I have the answer to the question, but I can't seem to quite get to it successfully.

    Please & thank you =)

    Let f(x)= x^5 and g(x)= 2x-3, Find (g o f)(x) and (g o f)'x

    -Finding (g o f)(x) -->
    f(x) = x^5
    g(x^5)= 2x^5-3
    Which is the correct answer for part 1

    -Finding (g o f)'(x) -->
    g'(f(x))(f'(x))
    g'(x^5)(5x^4)
    10x^4 * 5x^4
    = 50x^8
    But the answer 10x^4
    The best approach is to just write out the composite function and differentiate. If f(x)=x^5 and g(x)=2x-3, then g(f(x))=2(x^5)-3.

    If you differentiate this, you should get 10x^4.
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