What is the d/(dy)(ln(x-2y)) ?

The d/(dy)(ln(x-2y)) is -2/(x-2y)

What is the first d/(dy)(ln(x-2y)) ?

The first d/(dy)(ln(x-2y)) is -2/(x-2y)

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\frac{d}{d y} (ln (x - 2 y))

- \frac{2}{x - 2 y}

Solution steps

\frac{d}{d y} (ln (x - 2 y))

Treat

x

as a constant

Apply the chain rule:

\frac{1}{x - 2 y} \frac{d}{d y} (x - 2 y)

= \frac{1}{x - 2 y} \frac{d}{d y} (x - 2 y)

\frac{d}{d y} (x - 2 y) = - 2

= \frac{1}{x - 2 y} (- 2)

Simplify

\frac{1}{x - 2 y} (- 2) : - \frac{2}{x - 2 y}

= - \frac{2}{x - 2 y}

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\frac{d}{d x} (ln (ln (9 x)))

\int_{0}^{9} 2 π y (3 - \frac{y}{3}) d y