Question

Suppose that f and g are functions that are differentiable at x = 1 and that f(1) = 2, f '(1) = −1, g(1) = −2, and g'(1) = 3. Find h'(1).

h(x) = (x2 + 1)g(x)

Answer 1

h'(x)=(x^2+1)g'(x)+2xg(x).

h'(1)=2g'(1)+2g(1)=6+(-4)=2.