What is (\partial)/(\partial y)(ln(x-5y)) ?

The answer to (\partial)/(\partial y)(ln(x-5y)) is -5/(x-5y)

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(\partial)/(\partial y)(ln(x-5y))

\frac{\partial}{\partial y} (ln (x - 5 y))

- \frac{5}{x - 5 y}

Solution steps

\frac{\partial}{\partial y} (ln (x - 5 y))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{x - 5 y} \frac{\partial}{\partial y} (x - 5 y)

= \frac{1}{x - 5 y} \frac{\partial}{\partial y} (x - 5 y)

\frac{\partial}{\partial y} (x - 5 y) = - 5

= \frac{1}{x - 5 y} (- 5)

Simplify

\frac{1}{x - 5 y} (- 5) : - \frac{5}{x - 5 y}

= - \frac{5}{x - 5 y}

What is (\partial)/(\partial y)(ln(x-5y)) ?
The answer to (\partial)/(\partial y)(ln(x-5y)) is -5/(x-5y)