What is (\partial)/(\partial x)(ln(5x)) ?

The answer to (\partial)/(\partial x)(ln(5x)) is 1/x

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(\partial)/(\partial x)(ln(5x))

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

\frac{1}{x}

Solution steps

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

Apply the chain rule:

\frac{1}{5 x} \frac{\partial}{\partial x} (5 x)

= \frac{1}{5 x} \frac{\partial}{\partial x} (5 x)

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

= \frac{1}{5 x} \cdot 5

Simplify

\frac{1}{5 x} \cdot 5 : \frac{1}{x}

= \frac{1}{x}

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What is (\partial)/(\partial x)(ln(5x)) ?
The answer to (\partial)/(\partial x)(ln(5x)) is 1/x