What is (\partial)/(\partial z)(sqrt(xyz)) ?

The answer to (\partial)/(\partial z)(sqrt(xyz)) is (sqrt(x)sqrt(y))/(2sqrt(z))

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(\partial)/(\partial z)(sqrt(xyz))

\frac{\partial}{\partial z} (x yz)

\frac{x y}{2 z}

Solution steps

\frac{\partial}{\partial z} (x yz)

Treat

x, y

as constants

Apply the chain rule:

\frac{1}{2 x yz} \frac{\partial}{\partial z} (x yz)

= \frac{1}{2 x yz} \frac{\partial}{\partial z} (x yz)

\frac{\partial}{\partial z} (x yz) = x y

= \frac{1}{2 x yz} x y

Simplify

\frac{1}{2 x yz} x y : \frac{x y}{2 z}

= \frac{x y}{2 z}

\frac{d}{d x} (cos (\frac{π}{4}))

\frac{d}{d x} (lo g_{10} (arcsin (cos (x))))

\int \frac{sin ( 2 x )}{15 + cos ^{2} ( x )} d x

\int \frac{10}{x ^{2} - 1} d x

y = x^{\frac{1}{2}}, y = x - 2, [0, 4]

What is (\partial)/(\partial z)(sqrt(xyz)) ?
The answer to (\partial)/(\partial z)(sqrt(xyz)) is (sqrt(x)sqrt(y))/(2sqrt(z))