Question Video: Finding the Differentiation of a Given Inverse Function | Nagwa Question Video: Finding the Differentiation of a Given Inverse Function | Nagwa

# Question Video: Finding the Differentiation of a Given Inverse Function Mathematics • Higher Education

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

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### Video Transcript

If π of two π is equal to negative one, π prime of two π is equal to one, and π is equal to negative one, find the derivative of the inverse of π at π.

Weβll be using the fact that the derivative of the inverse of π at π is equal to one over π prime of π inverse of π. In our case, π is equal to negative one. We need to start by finding π inverse of negative one. Weβre given in the question that π of two π is equal to negative one. Since we know that π inverse is the inverse function of π, this tells us that π inverse of negative one is equal to two π. So we can substitute this into our equation. And now, we have that the derivative of π inverse at negative one is equal to one over π prime of two π. And we can see that weβve actually been given π prime of two π in the question. And itβs equal to one.

So we can substitute this in. And weβve reached our solution, which is that the derivative of the inverse function of π at negative one is equal to one.

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