Calculus: the derivative of an inverse function

The tutor shows the development of a formula for the derivative of an inverse.

Let’s imagine m(x) is a function with inverse m-1(x). Then

m(m-1(x)) = x

By implicit differentiation,

[m(m-1(x))]’ = 1

By the chain rule,

[m(m-1(x))]’ = m'(m-1(x))*(m-1(x))’

Therefore,

m'(m-1(x))*(m-1(x))’ = 1

Dividing both sides by m'(m-1(x)) yields

(m-1(x))’ = 1/m'(m-1(x))

In a coming post I’ll show an example of using this formula to find the derivative of a specific inverse function.

HTH:)

Source:

Larson, Roland E. and Robert P. Hostetler. Calculus, 3rd ed. Toronto: D C Heath and Company, 1989.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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