What is (\partial)/(\partial y)(xy+2x-ln(x^2y)) ?

The answer to (\partial)/(\partial y)(xy+2x-ln(x^2y)) is x-1/y

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(\partial)/(\partial y)(xy+2x-ln(x^2y))

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

x - \frac{1}{y}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (2 x) = 0

\frac{\partial}{\partial y} (ln (x^{2} y)) = \frac{1}{y}

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

Simplify

= x - \frac{1}{y}

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What is (\partial)/(\partial y)(xy+2x-ln(x^2y)) ?
The answer to (\partial)/(\partial y)(xy+2x-ln(x^2y)) is x-1/y