Question

17. Consider the function f(x, y, z) = xy ln(yz).

Compute the following partial derivatives:
(a) fx =
(b) fy =
(c) fz =​

Answer 1

We can expand

`f(x,y,z) = xy\ln(yz) = xy \ln(y) + xy\ln(z)`

Then using the product and chain rules,

`(\partial f)/(\partial x) = y\ln(y) + y\ln(z) + \boxed{y\ln(yz)}`

`(\partial f)/(\partial y) = x\ln(y) + \frac{xy}y + x\ln(z) = \boxed{x\ln(yz) + x}`

`(\partial f)/(\partial z) = \boxed{\frac{xy}z}`