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March 27, 2017

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i don't understand this problem
Let F(x)=f(x^4) and G(x)=(f(x))^4. You also know that a^3=2, f'(a)=13, f'(a^4)=15. Find F'(a) and G'(a).

  • COLLEGE CALCULUS. - ,

    F(x)=f(x^4)
    Using the chain rule,
    F'(x)=f'(x^4)*(d(x^4)/dx)=f'(x^4)*3x^3
    substitute x for a and all the numerical values supplied to find F'(a).

    Similarly, G(x)=(f(x))^4
    Apply the chain rule successively,
    G'(x)=(d/dx)(f(x))^4)
    =4f(x)^3*f'(x)
    So G'(a)=4f(a)^3*f'(a)
    Although f'(a) is known, it is not clear to me how we can find f(a).

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