SOLVED:Prove that a function has an inverse if and only if it is oneto-one.

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

Derivatives of Logarithmic Functions & Practice Problems