[GET ANSWER] Let f and g be inverse functions that are differentiable for all x. If f(3) = -2 and g'(-2) = -4, which of the following statements must be false?I. f'(0) = (1)/(4)II. f'(3) = -(1)/(4)III. f'(5) = -(1)/(4)

If y = f(x) is a differentiable function of x such that inverse function x = f^-1 (y) exists, then prove that x is a differentiable function of y and dxdy = 1 dydx where dydx≠ 0 .Hence find ddx(tan^-1x)

Inverse Function Theorem – Explanation & Examples - The Story of Mathematics - A History of Mathematical Thought from Ancient Times to the Modern Day