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

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

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

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

\frac{1}{x} + 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= 1 + 0 + \frac{1}{x}

Simplify

= \frac{1}{x} + 1

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