Sqrt(xyz)
I rewrote it has x^(1/2)*y^(1/2)+z^(1/2)
And the derivative with respect to x is
Sqrtyz/(2sqrtx) is that right
almost. You can't just toss away the x. Consider y and z as constants. You end up with
yz / 2√xyz
Also, √xyz is NOT √x√y + √z
However, if you consider
√x√y√z, then ∂f/∂x is
(√y√z) * 1/2√x as we saw at first.