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))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \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} \cdot 2

Simplify

- \frac{1}{2 x} \cdot 2 : - \frac{1}{x}

= - \frac{1}{x}

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