### Video Transcript

If π of π₯ is equal to negative
five π to the negative nine π₯, find π dash of π₯. Find the derivative of the
function.

Remember, the derivative of π to
the power of π₯ is π to the power of π₯. And the derivative of π to the
power of ππ₯ is ππ to the ππ₯. Now, our function is some multiple
of π to the ππ₯. Itβs negative five times π to the
ππ₯, where π is equal to negative nine. Now, we know that the constant
factor rule allows us to take constants outside a derivative and concentrate on
differentiating the function of π₯ itself. So this means we can say that the
derivative of the function of π₯ is equal to negative five times the derivative of
π to the negative nine π₯. And we know that the derivative of
π to the negative nine π₯ is negative nine times π to the negative nine π₯. And since negative five multiplied
by negative nine is 45, we can say that the derivative of our function is 45π to
the negative nine π₯.