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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