00:01
Here we are given f of x, y, z is equal to x to the fourth y plus z squared, where x of t is equal to s squared t, y of t is equal to s cubed t squared, and z of t is equal to s cubed t.
00:18
And we want to find the partial derivative of f with respect to s.
00:23
So this is going to equal the partial derivative of f with respect to x, and then the partial derivative of x with respect to s.
00:31
Then plus the partial of f with respect to y, plus the partial of y with respect to s, and then also, sorry not plus, that's supposed to be multiplied here.
00:44
And then plus the partial of f with respect to z, times the partial of z with respect to s.
00:51
So the partial derivative of f with respect to x is going to equal 4x cubed y.
00:58
And then we are going to multiply that by the partial derivative of x with respect to s, which is going to be 2st...