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

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

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

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

\frac{1}{y + 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) = 1

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

Simplify

= \frac{1}{y + x}

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