### Video Transcript

Let π be the inverse of π. Using the values in the table, find π prime of one. And weβve been given a table of values that tells us when π₯ is one, the value of π of π₯ is negative five and the value of the inverse of π π of π₯ is two and when π₯ is one, the first derivative of π is negative two. Similarly, when π₯ is two we have that π of π₯ is negative nine, π of π₯ is four, and the first derivative of π at π₯ equals two is one.

So weβre looking for π prime of one where π is the inverse function of π. So we can use the formula for derivatives of inverse functions. That is, for a function π with inverse π, we have that π prime of π¦ equals one over π prime of π of π¦. And this is valid, provided that the denominator is not equal to zero. So because weβre trying to find π prime of one, letβs replace π¦ with one in the formula. So for this composite function on the denominator π prime of π of one, letβs work from the inside out.

So letβs, firstly, find the value of π of one. We can find this information in the table. When π₯ is one, π of π₯ is two. So π of one is two, which means that we now need to find one over π prime of two. So letβs use the table weβre given in the question. When π₯ is two, we have that π prime of π₯ is one. So π prime of two is one, which gives us that π prime of one is equal to one over one, which is of course one.