00:01
In this problem, we're given the equation, y equals x cubed over 3, lnx minus x cubed over 9.
00:09
And we're asked to find the derivative of y with respect to x.
00:13
So to find the derivative of this equation, we're going to find the derivative of each part.
00:17
So that's finding the derivative of x cubed over 3, lnx, and the derivative of x cubed over 9.
00:23
So to find the derivative of x cubed over 3, lnx, we're going to use the product rule.
00:29
And this is used when finding the derivative of a function that can be expressed as the product of two different functions.
00:39
And this is written as ddx of f of x times g of x equals f of x times g prime of x plus g of x times f prime of x.
01:02
And so if we look at x cubed over 3 l and x, we see that this can be written as the product of two different functions.
01:13
So that this is x cubed over 3 times lnx...