Question

x 1 2 3 4
f(x) 0 1 2 3
g(x) -1 -2 -4 -5
f'(x) 4 3 5 6
g'(x) -3 0 -2 1

compute (g of f)' (4)

Answer 1

I hope I'm understanding what is meant by (g of f)'(4). Here goes:
let h(x) = g(f(x))
h'(x) = g'(y) f'(x) evaluated at y=f(x) (chain rule)
For x=4 this is
h'(4) = g'(f(4)) f'(4)
= g'(3) f'(4)
= -2 (6)
= -12

Answer 2

thats right. thanks for the help

Answer 3

oh, good. you're welcome.