Give that Hx g fx and f1 2 f1 4 f2 3 f2 4 g3 1 and g3

Give that H(x) = (g f)(x) and f(1) = 2, f\'(1) = 4, f(2) = -3, f\'(2) = 4, g(-3) -= 1 and g\'(-3) = 3, find H\'(2).

Solution

Given that

h(x) = {gof}(x)

Hence by chain rule differentiation

h\'(x) = g\'{f(x)}f\'(x)

Substitute x =2

h\'(2) =  g\'{f(2)}f\'(2)

f\'(2) = 4 and f(2) = -3

g\'(-3) = 3

Substitute to get

h\'(2) = 3(-3)

= -9