What is (\partial)/(\partial x)(yln(xy)) ?

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

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(\partial)/(\partial x)(yln(xy))

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

\frac{y}{x}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{y}{x}

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