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.
Weβll 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. Weβre 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 weβve actually
been given π prime of two π in the question. And itβs equal to one.
So we can substitute this in. And weβve reached our solution,
which is that the derivative of the inverse function of π at negative one is equal
to one.
