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

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

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(\partial)/(\partial x)(ln(yx))

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

\frac{1}{x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{y x} y

Simplify

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

= \frac{1}{x}

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