00:10
We're going to find the derivative of this function, so we're going to do the limit as x approaches h of k of x plus h minus k of x all over h.
00:22
Now we know k of x, which is this, so that's going to go in there.
00:27
And we have to figure out this k of x plus h.
00:31
So for that, oh, that's an x.
00:35
We're going to put x plus h in place of each x.
00:40
In the fraction.
00:43
So that gives us the limit.
00:45
Each approach is zero of x plus h plus 3 over x plus h minus the k of x, x plus 3 over x, and that's all over h.
00:59
So for the numerator we want each of these fractions to get a common denominator, which will be both of our denominators multiplied together.
01:10
Like so.
01:12
So the first fraction, you have to multiply top and bottom by x to get that common denominator.
01:19
So let's distribute that x, x squared plus x, h plus 3x.
01:26
The second fraction you have to multiply top and bottom by x plus h to get that common denominator.
01:32
So we're going to foil, that's x squared plus xh plus 3x...