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

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

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

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

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derivative of

3 ln (2 x)

\frac{3}{x}

Solution steps

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

Take the constant out:

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

= 3 \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

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

Simplify

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

= \frac{3}{x}

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

\frac{d}{d x} (1 0^{6} \cdot x^{2} \cdot e^{- x})

\int \frac{e ^{2 t}}{e ^{2 t} + 4} d t

\frac{d}{d y} (10 e^{x} sin (y) z^{3})

\frac{d}{d t} (5 t^{- \frac{3}{5}})

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