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, where we have that w equals ze to the power of x over y, x equals s minus t, y equals s plus t, and z z equals s times t.
00:15
So to begin, we'll find the partial derivatives of w with respect to x, y, and z, where we have that wx will be equal to z, e to the power of x over y, divided by y, which then in turn, when we substitute in what we have for x and y, we get that we can express this as s times t times e to the power of s minus t over s plus t, all divided by s plus t.
00:43
Wy then will be equal to negative x z, e to the power of x over y, all divided by y squared, which when we make the appropriate substitution, we'll have that this becomes negative t, s times s minus t, times e to the power of s minus t over s plus t, divided by s plus t all squared.
01:08
And lastly, wz will be equal to e to the power of x over y, which then will simply be e to the power of s minus t over s plus t.
01:22
Now we what we want to do next is find the partial derivatives of x, y, and z with respect to s and t...