What is (\partial)/(\partial y)(ln(x-6y)) ?

The answer to (\partial)/(\partial y)(ln(x-6y)) is -6/(x-6y)

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(\partial)/(\partial y)(ln(x-6y))

\frac{\partial}{\partial y} (ln (x - 6 y))

- \frac{6}{x - 6 y}

Solution steps

\frac{\partial}{\partial y} (ln (x - 6 y))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{x - 6 y} \frac{\partial}{\partial y} (x - 6 y)

= \frac{1}{x - 6 y} \frac{\partial}{\partial y} (x - 6 y)

\frac{\partial}{\partial y} (x - 6 y) = - 6

= \frac{1}{x - 6 y} (- 6)

Simplify

\frac{1}{x - 6 y} (- 6) : - \frac{6}{x - 6 y}

= - \frac{6}{x - 6 y}

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What is (\partial)/(\partial y)(ln(x-6y)) ?
The answer to (\partial)/(\partial y)(ln(x-6y)) is -6/(x-6y)