Sqrt(xyz)

Question

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

Answer 1

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.