Find F'(a) and G'(a)?

Let F(x)= f(x^3) and G(x)= (f(x))^3

You also know that

a^2=2

f(a)= 2

f ‘(a)=14

f ‘(a^3)=15

Top 1 Answers

A few days ago

Anonymous

Favorite Answer

This is a Chain Rule question. If

F(x) = f(x^3),

then

F'(x) = 3x^2 f'(x)

So, F'(a) = 3a^2 f'(a) = 3(2)(14) = 84

For G'(x), you use the Power Rule, which is a special case of the Chain Rule:

G'(x) = 3(f(x)^2)f'(x^3)

So G'(a) = 3(f(a)^2)f'(a^3) = 3(2^2)(15) = 3(4)(15) = 180

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