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} (- 3)

Simplify

\frac{1}{x - 3 y} (- 3) : - \frac{3}{x - 3 y}

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

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