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

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

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(\partial)/(\partial x)(ln(xy))

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

\frac{1}{x}

Solution steps

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

Treat

y

as a constant

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

= \frac{1}{x y} y

Simplify

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

= \frac{1}{x}

\frac{d}{d x} (x^{3} e^{- x})

x \to 9 lim (x + 7)

\frac{d}{d t} (1 0^{2 t})

\frac{d}{d x} (3^{t} (5 t^{4} + 7 t + y (t, x) (t, x)^{4}))

y = x^{\frac{2}{5}} (x + 3)

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