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

The derivative of ln(x+sqrt(x^2+3)) is 1/(sqrt(x^2+3))

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

The first derivative of ln(x+sqrt(x^2+3)) is 1/(sqrt(x^2+3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{1}{x ^{2} + 3}

Solution steps

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

Apply the chain rule:

\frac{1}{x + x ^{2} + 3} \frac{d}{d x} (x + x^{2} + 3)

= \frac{1}{x + x ^{2} + 3} \frac{d}{d x} (x + x^{2} + 3)

\frac{d}{d x} (x + x^{2} + 3) = 1 + \frac{x}{x ^{2} + 3}

= \frac{1}{x + x ^{2} + 3} (1 + \frac{x}{x ^{2} + 3})

Simplify

\frac{1}{x + x ^{2} + 3} (1 + \frac{x}{x ^{2} + 3}) : \frac{1}{x ^{2} + 3}

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

What is the derivative of ln(x+sqrt(x^2+3)) ?
The derivative of ln(x+sqrt(x^2+3)) is 1/(sqrt(x^2+3))
What is the first derivative of ln(x+sqrt(x^2+3)) ?
The first derivative of ln(x+sqrt(x^2+3)) is 1/(sqrt(x^2+3))