00:01
All right, here we have our function, f of x, equals x times a square root of 2 minus x squared.
00:07
We want to find its derivative.
00:09
So first i'm going to write it as x times 2 minus x squared to the 1⁄2 power.
00:15
And then to find the derivative, we're going to use the product rule.
00:19
So what we see here is the first times the derivative of the second.
00:23
And when we take the derivative of the second, we're using the chain rule.
00:27
So what we see here is the derivative of the 1 .5 power part, the outside function.
00:32
Bring down the one -half, and we raise the inside to the negative one -half.
00:36
And then what we see here is the derivative of the inside.
00:39
The derivative of negative x squared would be negative 2x.
00:43
And then moving along, we have the second times the derivative of the first.
00:48
The derivative of x is just one.
00:50
And then we can simplify that derivative a little bit.
00:53
So what we can do is change our negative one -half power back to a radical and put it in the denominator, since we have a negative power...