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,
weβll 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¦. Weβre 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.