What is (\partial)/(\partial y)(ln(x+3y)) ?

The answer to (\partial)/(\partial y)(ln(x+3y)) is 3/(x+3y)

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(\partial)/(\partial y)(ln(x+3y))

\frac{\partial}{\partial y} (ln (x + 3 y))

\frac{3}{x + 3 y}

Solution steps

\frac{\partial}{\partial y} (ln (x + 3 y))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{x + 3 y} \frac{\partial}{\partial y} (x + 3 y)

= \frac{1}{x + 3 y} \frac{\partial}{\partial y} (x + 3 y)

\frac{\partial}{\partial y} (x + 3 y) = 3

= \frac{1}{x + 3 y} \cdot 3

Simplify

\frac{1}{x + 3 y} \cdot 3 : \frac{3}{x + 3 y}

= \frac{3}{x + 3 y}

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What is (\partial)/(\partial y)(ln(x+3y)) ?
The answer to (\partial)/(\partial y)(ln(x+3y)) is 3/(x+3y)