What is (\partial)/(\partial x)(ln(x*y)) ?

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

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(\partial)/(\partial x)(ln(x*y))

\frac{\partial}{\partial x} (ln (x \cdot 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}

X^{\frac{9}{6}}, 8, 5

\int \frac{( 8 x - 3 )}{x ^{2} + x + 1} d x

n = 1 \sum \infty 2^{n} - 3

\frac{d}{d x} (8^{x^{3}})

\frac{d y}{d t} = 4 y + y^{3}

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