What is the derivative of ln((2x/3)) ?

The derivative of ln((2x/3)) is 1/x

What is the first derivative of ln((2x/3)) ?

The first derivative of ln((2x/3)) is 1/x

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\frac{d}{d x} (ln (\frac{2 x}{3}))

\frac{1}{x}

Solution steps

\frac{d}{d x} (ln (\frac{2 x}{3}))

Apply the chain rule:

\frac{1}{\frac{2 x}{3}} \frac{d}{d x} (\frac{2 x}{3})

= \frac{1}{\frac{2 x}{3}} \frac{d}{d x} (\frac{2 x}{3})

\frac{d}{d x} (\frac{2 x}{3}) = \frac{2}{3}

= \frac{1}{\frac{2 x}{3}} \cdot \frac{2}{3}

Simplify

\frac{1}{\frac{2 x}{3}} \cdot \frac{2}{3} : \frac{1}{x}

= \frac{1}{x}

What is the derivative of ln((2x/3)) ?
The derivative of ln((2x/3)) is 1/x
What is the first derivative of ln((2x/3)) ?
The first derivative of ln((2x/3)) is 1/x