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}

x^{2} + 4 x + 3, y = - 2, - 2 < x < 0

51

x = y + 2, x = y^{2}

\frac{1}{7 - 6 e ^{x}}

\frac{\partial}{\partial x} (- 400 x (y - x^{2}) - 2 (1 - x))

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