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

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

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

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

\frac{1}{y}

Solution steps

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

Simplify

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

= \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}

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

\int \frac{x}{x + 7} d x

\frac{\partial}{\partial y} ((x + y)^{8})

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

x \to 2 lim (x^{2} + x - 2)

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