What is (\partial)/(\partial x)(ln(x/(2y))) ?

The answer to (\partial)/(\partial x)(ln(x/(2y))) is 1/x

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(\partial)/(\partial x)(ln(x/(2y)))

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

\frac{1}{x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x}

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What is (\partial)/(\partial x)(ln(x/(2y))) ?
The answer to (\partial)/(\partial x)(ln(x/(2y))) is 1/x