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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

2 ln (3 x)

\frac{2}{x}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2}{x}

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