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

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

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

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

\frac{e ^{x}}{y}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

= e^{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

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

Simplify

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

= \frac{e ^{x}}{y}

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