00:01
In this question we are given f of x, y, z which is equal to y square z tan cube x tan cube x and the point given is pi by 4 minus 3 and 1.
00:20
We have to find out the gradient of f at this point.
00:24
Now gradient of f is equal to del f by del x that is partial derivative of f with respect to x then with respect to y with respect to y and with respect to z.
00:41
So let us find out the values of del f by del x, y and z.
00:46
So del f by del y.
00:48
Now while differentiating partially with respect to x we will consider y and z to be constant.
00:54
So this will be 3 y square z tan square y tan square x and derivative of tan is sec square x.
01:06
Similarly let's differentiate it with respect to y as well.
01:09
So we will consider x and z to be constant now.
01:12
So this will be 2 y z tan cube x.
01:17
Similarly let us differentiate with respect to z.
01:21
So this will be y square tan cube x.
01:24
Now we have to find out the gradient at this point...