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Thread: chain rule question

  1. #1
    Junior Member
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    chain rule question

    hi guys
    just a quick check to make sure im getting this right

    $\displaystyle h(x)=f(g(x))$
    where $\displaystyle f(x) = x^5$ and $\displaystyle g(x)=x^2+1$
    so $\displaystyle h(x)=(x^2+1)^5$

    $\displaystyle h'(x)=5(x^2+1)^4(2x)$ <---- heheh everyone noticed the type. Yes i meant h not f XD

    now heres the part that confuses me. Is it correct to multiply the 5 before the brackets by the 2x to get
    $\displaystyle 10x(x^2+1)^4$?

    Help appreciated
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  2. #2
    Senior Member topher0805's Avatar
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    $\displaystyle h(x)=f(g(x))$
    where $\displaystyle f(x) = x^5$ and $\displaystyle g(x)=x^2+1$
    so $\displaystyle h(x)=(x^2+1)^5$

    $\displaystyle f'(x)=5(x^2+1)^4(2x)$
    I assume that you meant:

    $\displaystyle h'(x)=5(x^2+1)^4(2x)$

    Yes, you can multiply the $\displaystyle 5$ and the $\displaystyle 2x$ together. There is no rule against simplifying a derivative.
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