# Video: Differentiation for Inverse Functions

If π(1/2) = β6, πβ²(1/2) = 3, and π = β6, find (πβ»ΒΉ)β²(π).

01:31

### Video Transcript

If π of a half equals negative six, π prime of a half equals three, and π equals negative six, find the inverse of π prime of π.

Letβs start by recalling a useful formula for finding the derivative of an inverse function. That is the inverse of π prime of π equals one over π prime of the inverse of π of π. For our question, π equals negative six. So we can substitute this into the formula. So weβre going to need to find what π prime of the inverse of π of negative six is. Well, we can find what the inverse of π of negative six is using the information in the question and the definition of the inverse function.

The definition of the inverse function says that π of the inverse of π of π equals π. And so π of the inverse of π of negative six equals negative six. From the information given in the question, π of one-half equals negative six. So the inverse of π of negative six must be equal to a half. If we substitute this back into our workings, we find that the inverse of π prime of negative six equals one over π prime of one-half. From the question, weβre told that π prime of one-half equals three. And so we find that the inverse of π prime of negative six equals one over three.