What is (\partial)/(\partial x)(2sqrt(xyz)) ?

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

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(\partial)/(\partial x)(2sqrt(xyz))

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

\frac{y z}{x}

Solution steps

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

Treat

y, z

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

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

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

Simplify

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

= \frac{y z}{x}

y = \frac{3 x}{x}

\int \frac{ln ^{6} ( x )}{x} d x

x \to 0 lim (\frac{3 sin ( x ) + x}{x})

\int \frac{1}{3 x ( 5 + x )} d x

y = x^{4} + 7 e^{x}, (0, 7)

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