00:03
In this problem, we wish to find the derivative f prime x for f of x equals x cubed minus x over x.
00:08
This question is challenging your understanding of differentiation.
00:11
In particular, it's challenging your knowledge of derivative shortcuts.
00:14
Specifically, those derivative shortcuts we've learned are the rules through 1 through 5 here, they respectively the constant rule, the power rule, constant multiple rule, some difference rule, and exponential derivative rule.
00:26
Thus, to solve, we need to utilize these five rules in combination to solve for f prime x.
00:32
First, if we distribute the x here in the denominator of f of x, we can move out of f of x as x squared minus 1.
00:37
From this, we see that we have to use the sum difference rule, power rule, and constant rule to solve...