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

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

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(\partial)/(\partial x)(ln(x/k))

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

\frac{1}{x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x}

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