What is (\partial)/(\partial x)(ln(x/4)) ?

The answer to (\partial)/(\partial x)(ln(x/4)) is 1/x

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(\partial)/(\partial x)(ln(x/4))

\frac{\partial}{\partial x} (ln (\frac{x}{4}))

\frac{1}{x}

Solution steps

\frac{\partial}{\partial x} (ln (\frac{x}{4}))

Apply the chain rule:

\frac{1}{\frac{x}{4}} \frac{\partial}{\partial x} (\frac{x}{4})

= \frac{1}{\frac{x}{4}} \frac{\partial}{\partial x} (\frac{x}{4})

\frac{\partial}{\partial x} (\frac{x}{4}) = \frac{1}{4}

= \frac{1}{\frac{x}{4}} \cdot \frac{1}{4}

Simplify

\frac{1}{\frac{x}{4}} \cdot \frac{1}{4} : \frac{1}{x}

= \frac{1}{x}

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What is (\partial)/(\partial x)(ln(x/4)) ?
The answer to (\partial)/(\partial x)(ln(x/4)) is 1/x