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

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

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

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

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derivative of

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

\frac{1}{x}

Solution steps

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

Simplify

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

= \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}

\frac{d}{d x} (20 x^{2} + \frac{180}{x})

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

\frac{d y}{d θ} = 4 y^{2} sec^{2} (2 θ)

\frac{d}{d x} (lo g_{11} (x))

\int \frac{3 x ^{2}}{( x ^{2} + 1 ) ( x + 1 )} d x

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