Let y = f (x) be a function of x and suppose that we can solve this equation fcr x in terms of y so that we may write x as a function of y, say

x = g (y).

Then g (y) is called the inverse of f (x). The following result describes the relationship between dy/dx and dx/dy.

Let y = f (x) be a function which admits of an inverse function x = g (y). Let y = f (x) be differentiable at x such that f ‘(x) ≠  0. Then x = g (y) is differentiable at the corresponding value of y and dx/dy = 1/dy/dx.

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