What is the derivative of ln(x^2+6) ?

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

What is the first derivative of ln(x^2+6) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

ln (x^{2} + 6)

\frac{2 x}{x ^{2} + 6}

Solution steps

\frac{d}{d x} (ln (x^{2} + 6))

Apply the chain rule:

\frac{1}{x ^{2} + 6} \frac{d}{d x} (x^{2} + 6)

= \frac{1}{x ^{2} + 6} \frac{d}{d x} (x^{2} + 6)

\frac{d}{d x} (x^{2} + 6) = 2 x

= \frac{1}{x ^{2} + 6} \cdot 2 x

Simplify

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

= \frac{2 x}{x ^{2} + 6}

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