Differentiation

Question

If 𝑔 is a function satisfying 𝑔(3)=𝑔′(3)=−2, and ℎ(𝑥)=tan^−1[𝑔(𝑥)]. then what is ℎ′(3)?

Answer 1

h(x) = tan^-1(g(x))

Using the Chain Rule, h'(x) = [1 / (1 + (g(x))²] g'(x)

So, h'(3) = [1 / (1 + (-2)²] (-2) = -2/5