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Math Help - Differentiable functions.

  1. #1
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    Differentiable functions.

    There's an annotation when it comes to differentiable functions that confuses me and I'm not sure what the difference is.

    One is f(x)={\sqrt(f(x)) } and the other is f(x)=f{\sqrt(x) }.

    I know how to find the derivative of the first, but how is the second one different, and how do you find its derivative?
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  2. #2
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    Quote Originally Posted by Rumor View Post
    There's an annotation when it comes to differentiable functions that confuses me and I'm not sure what the difference is.

    One is f(x)={\sqrt(f(x)) } and the other is f(x)=f{\sqrt(x) }.

    I know how to find the derivative of the first, but how is the second one different, and how do you find its derivative?
    I assume for the second you mean f(\sqrt{x}).

    If so, simply use the chain rule. Let g(x) = \sqrt{x}, u(x) = f(g(x)), then:

    u'(x) = f'(g(x))\cdot g'(x)
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