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

The derivative of 3ln(x^2) is 6/x

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

The first derivative of 3ln(x^2) is 6/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{6}{x}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

= \frac{1}{x ^{2}} \frac{d}{d x} (x^{2})

\frac{d}{d x} (x^{2}) = 2 x

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

Simplify

3 \cdot \frac{1}{x ^{2}} \cdot 2 x : \frac{6}{x}

= \frac{6}{x}

What is the derivative of 3ln(x^2) ?
The derivative of 3ln(x^2) is 6/x
What is the first derivative of 3ln(x^2) ?
The first derivative of 3ln(x^2) is 6/x