What is (\partial)/(\partial x)(xyzsqrt(x)) ?

The answer to (\partial)/(\partial x)(xyzsqrt(x)) is (3yzsqrt(x))/2

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(\partial)/(\partial x)(xyzsqrt(x))

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

\frac{3 yz x}{2}

Solution steps

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

Simplify

x yz x : yz x^{\frac{3}{2}}

= \frac{\partial}{\partial x} (yz x^{\frac{3}{2}})

Treat

y, z

as constants

Take the constant out:

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

= yz \frac{\partial}{\partial x} (x^{\frac{3}{2}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= yz \frac{3}{2} x^{\frac{3}{2} - 1}

Simplify

yz \frac{3}{2} x^{\frac{3}{2} - 1} : \frac{3 yz x}{2}

= \frac{3 yz x}{2}

What is (\partial)/(\partial x)(xyzsqrt(x)) ?
The answer to (\partial)/(\partial x)(xyzsqrt(x)) is (3yzsqrt(x))/2