What is the derivative of ln(x+sqrt(x^2-8)) ?

The derivative of ln(x+sqrt(x^2-8)) is 1/(sqrt(x^2-8))

What is the first derivative of ln(x+sqrt(x^2-8)) ?

The first derivative of ln(x+sqrt(x^2-8)) is 1/(sqrt(x^2-8))

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} - 8))

\frac{1}{x ^{2} - 8}

Solution steps

\frac{d}{d x} (ln (x + x^{2} - 8))

Apply the chain rule:

\frac{1}{x + x ^{2} - 8} \frac{d}{d x} (x + x^{2} - 8)

= \frac{1}{x + x ^{2} - 8} \frac{d}{d x} (x + x^{2} - 8)

\frac{d}{d x} (x + x^{2} - 8) = 1 + \frac{x}{x ^{2} - 8}

= \frac{1}{x + x ^{2} - 8} (1 + \frac{x}{x ^{2} - 8})

Simplify

\frac{1}{x + x ^{2} - 8} (1 + \frac{x}{x ^{2} - 8}) : \frac{1}{x ^{2} - 8}

= \frac{1}{x ^{2} - 8}

What is the derivative of ln(x+sqrt(x^2-8)) ?
The derivative of ln(x+sqrt(x^2-8)) is 1/(sqrt(x^2-8))
What is the first derivative of ln(x+sqrt(x^2-8)) ?
The first derivative of ln(x+sqrt(x^2-8)) is 1/(sqrt(x^2-8))