What is (\partial)/(\partial y)(xln(xy)) ?

The answer to (\partial)/(\partial y)(xln(xy)) is x/y

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(\partial)/(\partial y)(xln(xy))

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

\frac{x}{y}

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

x \frac{1}{x y} x : \frac{x}{y}

= \frac{x}{y}

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What is (\partial)/(\partial y)(xln(xy)) ?
The answer to (\partial)/(\partial y)(xln(xy)) is x/y