00:01
For this problem, we are asked to find dw by ds and dw by dt by dt by using the appropriate chain rule for w equals x, kose of y, z, x equals s squared, and z equals s minus 2t.
00:13
Now, the first step that i'm going to take here is to find the partial derivative of w with respect to x, which will be cos times y, z, which then we can write as cos of s minus, or s minus 2t times t squared.
00:30
Then wy, which will be equal to, excuse me, it will be equal to negative xz times sine of yz, which upon substituting back in what we have for x, y, and z, this becomes negative s cubed times sine of, or actually, let me correct myself here, there would be an easier way to write this.
00:54
So it would be, we can write this as 2s squared t minus s cubed times sine.
01:01
Of 2 s or excuse me time sign of s minus 2t times t squared then taking the partial derivative with respect to z we get negative x times y times sine of y times z which will then give us negative s squared times t squared so negative s squared t squared and sine of t squared times s minus 2 t.
01:37
Then we want to find the partial derivatives of x, y, and z with respect to s and t...