00:01
In this problem, we are going to compute the differential of z equals sequence squared of x minus 3y.
00:08
And to do so, recall that if we have a function of two variables, just like in this case, a function of x and y, then the differential of z is equal to the partial derivative of z with respect to x, dx, plus the partial derivative of z, with respect to x, dx, plus the partial derivative of z with respect to y, d y.
01:06
So to find the differential of z, we just have to find the first order partial derivatives.
01:13
So let's go ahead and start there.
01:18
When we find the partial derivative of z with respect to x, we'll treat y as a constant.
01:30
So we can just imagine x minus 3y.
01:33
This minus 3y is just a number.
01:38
So in doing that, we get that this is equal to 2 times secant of x minus 3y, which i will highlight x just to emphasize our point times secant of x minus 3y, times tangent of x minus 3y.
02:30
And to compute this derivative, we're using chain rule and also using the fact that the derivative of secant is secant tangent...