00:01
So in this problem we are given the following function.
00:03
We're given f of x to equal to 1 over the cube root of x squared minus 1.
00:17
I'm going to rewrite this as x squared minus 1 all of this to the power of negative 1 over 3.
00:26
So by using this, note that i'm using the fact that the cube root of x squared minus 1 is the same as x squared minus 1 to the power of 1 over 3.
00:41
But because the power of 1 over 3 was on the bottom, we pretty much wrote that to a power of negative 1 over 3 on the numerator.
00:50
Alright, next i'm going to use the general power rule.
00:54
So the general power rule is as follows.
01:02
If you're trying to find the derivative, say with respect to x, of some function f of x raised to the power of n, then the rule tells us to bring the power of n down.
01:14
So that's going to give us n, the new power.
01:16
So f of x is raised to the new power of n minus 1 and multiplying everything by the derivative of the function f which is the input function.
01:25
So let's keep that in mind...