(chain rule) Let F ( x ) = f ( f ( x ) ) and G ( x ) = ( F ( x ) ) 2 . You also know that f ( 6 ) = 11 , f ( 11 ) = 3 , f ' ( 11 ) | = 7 , f ' ( 6 ) = 4

Question

Let  and  .You also know that Find     and   _____ 

Answer 1

F'(x) = f'(f(x))*f'(x) (Chain Rule)

F'(6) = f'(f(6))*f'(6) = f'(11)*4 = 7*4 = 28

(I am assuming you meant G(x) = (F(x))^2)

G'(x) = 2F(x)*F'(x) (Chain Rule again since F(x) is a function then you have a function inside the function (_)^2)

G'(6) = 2F(6)*F'(6) = 2*f(f(6))*28 = 2*f(11)*28 = 2*3*28 = 168

Please contact me if you need further explanation!