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

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

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(\partial)/(\partial y)(ln(xy))

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

\frac{1}{y}

Solution steps

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

Treat

x

as a constant

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

= \frac{1}{x y} x

Simplify

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

= \frac{1}{y}

\int x^{2} 3 - 2 x d x

\int \frac{1}{( a ^{2} + v ^{2} )} d v

y^{^{'}} + tan (x) y - sin (x) = 0

\int \frac{1}{x} + 2 x d x

\frac{\partial}{\partial x} (4 sin (4 x))

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