If f is a function satisfying f(3)=f′(3)=−2 , and j(x)=tan−1[f(x)] , then what is j′(3) ?

Answer 1

j(x) = Tan^-1(f(x))

By the Chain Rule, j'(x) = (1 / [1 + (f(x))²] ) f'(x)

So, j'(3) = (1 / [1 + 4])(-2) = -2/5