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

The answer to (\partial)/(\partial x)(sqrt(2x)) is 1/(sqrt(2)\sqrt{x)}

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

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

\frac{1}{2 x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 2 x} \cdot 2 : \frac{1}{2 x}

= \frac{1}{2 x}

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What is (\partial)/(\partial x)(sqrt(2x)) ?
The answer to (\partial)/(\partial x)(sqrt(2x)) is 1/(sqrt(2)\sqrt{x)}