00:01
Okay, for this problem, we're given the equation for y prime, which is given by x minus 2 over x to the third power plus 3.
00:12
The first thing we're going to do is rewrite this as x minus 2x to negative 3 plus 3.
00:20
And that's going to make it easier for us.
00:21
So we're asked to find the original function y, for which y is equal to f of x.
00:26
And to do that, we're going to use our power rules that we know for differentiation in a reverse order.
00:33
And later, it'll become a lot easier once we learn about the anti -derivative and we start getting the rules there.
00:39
I don't want to get too ahead of myself.
00:40
And so we're just going to creatively using what we know right now, which is just the derivative and the process of differentiation, as the chapter is conveniently named, we're going to try to work backwards.
00:51
So to find why, well, we're going to try to think about this.
00:54
When we find the derivative of x squared, given by this, we end up with 2x, right? and when we do the same thing for, let's say, x to the third power, we end up with 3x to the second power.
01:11
And so the first thing we'll notice is we have this drop.
01:13
And that's the most important thing.
01:15
We have this drop from 2 to 1, from 3 to 2...