Calculus help!!

Question

A certain differentiable function / has a tangent line y = pi/2 * x - pi/2 at the point on its graph where x = 1 If g is another function defined by g(x)= sin(3f(x)) +( tilde f (x))^ 2 ] what is g'(1)?

Answer 1

The line is tangent to y = f(x) at the point (1, 0). We have

g'(x) = cos[3f(x)]f'(x) + 2f(x)f'(x)

Hence

g'(1) = cos(0)(pi/2) + 0*(pi/2) = pi/2