What is the derivative of ln(-2x) ?

The derivative of ln(-2x) is 1/x

What is the first derivative of ln(-2x) ?

The first derivative of ln(-2x) is 1/x

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

\frac{1}{x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{x}

What is the derivative of ln(-2x) ?
The derivative of ln(-2x) is 1/x
What is the first derivative of ln(-2x) ?
The first derivative of ln(-2x) is 1/x