# Question Video: Finding the Value of an Inverse Function Mathematics • Higher Education

Let π be the inverse of π. Using the table below, find πβ²(0).

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### Video Transcript

Let π be the inverse of π. Using the table below, find π prime of zero.

In order to find π prime of zero, weβll be using the formula for finding the derivative of an inverse of a function. Which tells us that π prime of π¦ is equal to one over π prime of π of π¦. Weβre trying to find π prime of zero. So we can substitute in zero for π¦. This gives us that π prime of zero is equal to one over π prime of π of zero. From the table, we can see that when π₯ is equal to zero, π is equal to negative one. And so, we have that π of zero is equal to negative one. Which we can substitute in to give us that π prime of zero is equal to one over π prime of negative one.

And now, we can simply read π prime of negative one off from the table. Since when π₯ is equal to negative one, π prime is equal to one-third. Giving us that π prime of negative one is equal to one-third. And again, this can be substituted in. And so, we will obtain that π prime of zero is equal to the reciprocal of one-third. And here, we reach our solution of three.