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

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

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

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

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

- \frac{2}{x}

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - \frac{2}{x}

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