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

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

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

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

\frac{1}{x}

Solution steps

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

Simplify

ln (x) + ln (y) : ln (x y)

= \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}

\int x^{3} (8^{- x^{4}}) d x

\frac{d}{d x} ((2 x^{4} - 7 x^{3} + 2 x - 1)^{2})

\int x cos (nπ x) d x

x^{3} - 25 x + 5

\frac{d}{d x} (2 x^{3} - 11.7 x^{2} + 17.7 x - 5)

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