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

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

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(\partial)/(\partial x)(sqrt(xyz))

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

\frac{y z}{2 x}

Solution steps

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

Treat

y, z

as constants

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{y z}{2 x}

\int e^{- 2 x} (1 - 2 x) d x

\frac{d}{d x} (2^{0.25})

\frac{d}{d x} (sin (7 x) + cos (2 x))

\frac{\partial}{\partial x} (\frac{e ^{v}}{u ( v , x ) + v ^{9}})

x \to - 1 lim (- x^{2} + 7 x - 8)

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