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January 27, 2015

January 27, 2015

Posted by **LISA** on Monday, February 27, 2012 at 12:16am.

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).

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**MathMate**, Monday, February 27, 2012 at 9:16amF(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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