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Math Help - Differentiating given f(x)

  1. #1
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    Exclamation Differentiating given f(x)

    Given y=f(x) with f(1)=4 and f'(1)=3, find:
    A) g'(1) if g(x) = √(f(x))
    B) h'(1) if h(x) = f(√(x))
    And show how you got there so I can learn.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Differentiating given f(x)

    What have you tried? What is g'(x) and h'(x)?
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  3. #3
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    Re: Differentiating given f(x)

    These are both about using the chain rule.
    I'll use a function other than the square root to give you an idea.

    \text{A) Suppose } h(x) = [f(x)]^3

    \text{Then } h'(x) = 3[f(x)]^2f'(x)

    \text{so } h'(1) = 3[f(1)]^2f'(1) = 3[4]^2(3) = (9)(16) = 144.

    \text{B) Suppose } \alpha(x) = f(x^3)

    \text{Then } \alpha'(x) = f'(x^3)(3x^2)

    \text{so } \alpha'(1) = f'(1^3)(3(1^2)) = 3f'(1) = (3)(3) = 9.
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  4. #4
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    Re: Differentiating given f(x)

    Quote Originally Posted by johnsomeone View Post
    These are both about using the chain rule.
    I'll use a function other than the square root to give you an idea.

    \text{A) Suppose } h(x) = [f(x)]^3

    \text{Then } h'(x) = 3[f(x)]^2f'(x)

    \text{so } h'(1) = 3[f(1)]^2f'(1) = 3[4]^2(3) = (9)(16) = 144.

    \text{B) Suppose } \alpha(x) = f(x^3)

    \text{Then } \alpha'(x) = f'(x^3)(3x^2)

    \text{so } \alpha'(1) = f'(1^3)(3(1^2)) = 3f'(1) = (3)(3) = 9.
    Even better answer than I was expecting, now I can do it (and future problems) on my own, thank you.
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