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Math Help - 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

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

    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
    10x(x^2+1)^4?

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

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

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

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