00:01
In this question, if f of x, y, z equals yz times the ln of x, y, i want to find the partial derivative of f with respect to x, the partial of f with respect to y, and the partial of f with respect to z.
00:13
So let's start with our partial derivative of f with respect to x.
00:19
Now, yz is thought of as a constant.
00:22
If i'm taking the derivative with respect to x, then y and z are thought of as constants, and only x is thought of as the variable.
00:32
So we've got yz, that constant multiple, coming along for the ride.
00:36
The derivative of the ln of x, y would be 1 over x, y times the derivative of the inside, the derivative of x, y with respect to x.
00:49
That would be y.
00:51
Now, if i clean up a little bit, the y over y, that cancels, and i'm getting yz over x.
01:03
Next, i need my partial derivative of f with respect to y.
01:07
Now, both factors now involve y, and so therefore, i need the product rule.
01:14
The product rule says i start with my first factor, yz, times the derivative of the second factor...