What is (\partial)/(\partial x)(5sqrt(2x)) ?

The answer to (\partial)/(\partial x)(5sqrt(2x)) is 5/(sqrt(2)\sqrt{x)}

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(\partial)/(\partial x)(5sqrt(2x))

\frac{\partial}{\partial x} (5 2 x)

\frac{5}{2 x}

Solution steps

\frac{\partial}{\partial x} (5 2 x)

Simplify

5 2 x : 52 x

= \frac{\partial}{\partial x} (52 x)

Take the constant out:

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

= 52 \frac{\partial}{\partial x} (x)

Apply radical rule:

a = a^{\frac{1}{2}}

= 52 \frac{\partial}{\partial x} (x^{\frac{1}{2}})

Apply the Power Rule:

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

= 52 \frac{1}{2} x^{\frac{1}{2} - 1}

Simplify

52 \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{5}{2 x}

= \frac{5}{2 x}

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What is (\partial)/(\partial x)(5sqrt(2x)) ?
The answer to (\partial)/(\partial x)(5sqrt(2x)) is 5/(sqrt(2)\sqrt{x)}