00:01
These next four problems carry on from the previous ones.
00:04
And here again we're given, we want to find the derivative respect to x of f of sine of x.
00:11
So we have some function of sine of x in here.
00:17
Now, we can kind of find this as u.
00:20
So we get the f, d .u, d .x of sine of x, cosine of x.
00:27
And then this is f prime evaluated at u equals sine of x.
00:32
So we get cosine of x, f prime evaluated at sign of x.
00:39
Now we have d d d x of some function of the tangent of x.
00:44
So again we define this as you.
00:46
We get dfd u, the derivative of tangent of x, derivative of tangent of x is sequence squared of x.
00:56
And then we have f prime evaluated at tangent of x.
01:01
So again, where you can't go any further than this because we don't know what this function actually is.
01:08
Now they're getting a little, making a thing life a little difficult for us by having second derivatives.
01:16
So we want the second derivative of f, which is a function of cosine of x.
01:21
So how do we do that? well, we just peel off one derivative and do that.
01:27
So we pull out a ddx.
01:28
And then the first d -d -x is d -f -d -u -d -x.
01:33
The fdu is u prime evaluated at cosine of x and the udx is sign of x...