What is the derivative of 4ln(5x) ?

The derivative of 4ln(5x) is 4/x

What is the first derivative of 4ln(5x) ?

The first derivative of 4ln(5x) is 4/x

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\frac{d}{d x} (4 ln (5 x))

\frac{4}{x}

Solution steps

\frac{d}{d x} (4 ln (5 x))

Take the constant out:

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

= 4 \frac{d}{d x} (ln (5 x))

Apply the chain rule:

\frac{1}{5 x} \frac{d}{d x} (5 x)

= \frac{1}{5 x} \frac{d}{d x} (5 x)

\frac{d}{d x} (5 x) = 5

= 4 \cdot \frac{1}{5 x} \cdot 5

Simplify

4 \cdot \frac{1}{5 x} \cdot 5 : \frac{4}{x}

= \frac{4}{x}

What is the derivative of 4ln(5x) ?
The derivative of 4ln(5x) is 4/x
What is the first derivative of 4ln(5x) ?
The first derivative of 4ln(5x) is 4/x