What is (\partial)/(\partial x)(xy-ln(xy)) ?

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

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(\partial)/(\partial x)(xy-ln(xy))

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

y - \frac{1}{x}

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

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

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

= y - \frac{1}{x}

\frac{d}{d x} (\frac{( 6 x ^{2} + 4 )}{( 3 y ^{2} - 4 )})

\int_{- 3}^{0} 1 + 9 - x^{2} d x

\frac{200}{( s + 10 ) ( s + 100 )}

x^{^{''}} - x = 0

\frac{d}{d x} (x^{3} - 2 x^{2} + x - 20)

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