What is (\partial)/(\partial y)(ln(x+2y)) ?

The answer to (\partial)/(\partial y)(ln(x+2y)) is 2/(x+2y)

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(\partial)/(\partial y)(ln(x+2y))

\frac{\partial}{\partial y} (ln (x + 2 y))

\frac{2}{x + 2 y}

Solution steps

\frac{\partial}{\partial y} (ln (x + 2 y))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{x + 2 y} \frac{\partial}{\partial y} (x + 2 y)

= \frac{1}{x + 2 y} \frac{\partial}{\partial y} (x + 2 y)

\frac{\partial}{\partial y} (x + 2 y) = 2

= \frac{1}{x + 2 y} \cdot 2

Simplify

\frac{1}{x + 2 y} \cdot 2 : \frac{2}{x + 2 y}

= \frac{2}{x + 2 y}

f (x) = ln^{2} (x)

\frac{4}{1 + x}

\frac{d}{d x} (sin (2 x^{4}))

\frac{d}{d x} (\frac{1}{- sin ( x )})

What is (\partial)/(\partial y)(ln(x+2y)) ?
The answer to (\partial)/(\partial y)(ln(x+2y)) is 2/(x+2y)