What is the derivative of ln(2x)*4 ?

The derivative of ln(2x)*4 is 4/x

What is the first derivative of ln(2x)*4 ?

The first derivative of ln(2x)*4 is 4/x

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derivative of

ln (2 x) \cdot 4

\frac{4}{x}

Solution steps

\frac{d}{d x} (ln (2 x) \cdot 4)

Take the constant out:

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

= 4 \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

= 4 \cdot \frac{1}{2 x} \cdot 2

Simplify

4 \cdot \frac{1}{2 x} \cdot 2 : \frac{4}{x}

= \frac{4}{x}

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What is the derivative of ln(2x)*4 ?
The derivative of ln(2x)*4 is 4/x
What is the first derivative of ln(2x)*4 ?
The first derivative of ln(2x)*4 is 4/x