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

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

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(\partial)/(\partial y)(sqrt(xyz))

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

\frac{x z}{2 y}

Solution steps

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

Treat

x, z

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{x z}{2 y}

\int \frac{2 x}{4 - x ^{2}} d x

y^{^{''}} + 2 y = - 18 x^{2} e^{2} x

\frac{d}{d x} (- \frac{9}{( 1 + 3 x ) ^{2}})

y = x^{3} - 3 x^{2} + 3 x, y = x

\frac{d}{d x} (x^{2} - 7 x + 12)

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