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

The answer to (\partial)/(\partial x)(y/x+ln(y)) is -y/(x^2)

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

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

- \frac{y}{x ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial x} (\frac{y}{x}) = - \frac{y}{x ^{2}}

\frac{\partial}{\partial x} (ln (y)) = 0

= - \frac{y}{x ^{2}} + 0

Simplify

= - \frac{y}{x ^{2}}

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What is (\partial)/(\partial x)(y/x+ln(y)) ?
The answer to (\partial)/(\partial x)(y/x+ln(y)) is -y/(x^2)