What is the derivative of 3ln(15x) ?

The derivative of 3ln(15x) is 3/x

What is the first derivative of 3ln(15x) ?

The first derivative of 3ln(15x) is 3/x

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\frac{d}{d x} (3 ln (15 x))

\frac{3}{x}

Solution steps

\frac{d}{d x} (3 ln (15 x))

Take the constant out:

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

= 3 \frac{d}{d x} (ln (15 x))

Apply the chain rule:

\frac{1}{15 x} \frac{d}{d x} (15 x)

= \frac{1}{15 x} \frac{d}{d x} (15 x)

\frac{d}{d x} (15 x) = 15

= 3 \cdot \frac{1}{15 x} \cdot 15

Simplify

3 \cdot \frac{1}{15 x} \cdot 15 : \frac{3}{x}

= \frac{3}{x}

What is the derivative of 3ln(15x) ?
The derivative of 3ln(15x) is 3/x
What is the first derivative of 3ln(15x) ?
The first derivative of 3ln(15x) is 3/x