Let F(x)=f(x^7) and G(x)=(f(x))^7. You also know that a^6=12, f(a)=3, f’(a)=11 and f’(a^7)=10. Find F’(a) and G’(a).

Answer 1

F(x) = f(x⁷) and G(x) = (f(x))⁷

By the Chain Rule, F'(x) = f'(x⁷)(7x⁶) and G'(x) = 7(f(x))⁶f'(x)

So, F'(a) = f'(a⁷)(7a⁶) = (10)(7)(12) = 840 and G'(a) = 7(f(a))⁶f'(a) = 7(3)⁶(11)