What is (\partial)/(\partial x)(sqrt(x*y*z)) ?

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

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

\frac{\partial}{\partial x} (x \cdot y \cdot z)

\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}

x \to 4 + lim (\frac{( 7 x )}{x - 4})

\int \frac{8}{4 x ^{2} + 1} d x

y = 1 - x^{2}, y = 29 - 11 x

2 (3 x - 8)^{4} - 5 x + 6

x \to 1 + lim (cos (π x))

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