en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln(x+sqrt(x^2+1))

Solution

derivative of

ln (x + x^{2} + 1)

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches infinity of x/((ln(x))^3+2x)

x \to \infty lim (\frac{x}{( ln ( x ) ) ^{3} + 2 x})

2y(dy)/(dx)= x/(sqrt(x^2-16)),y(5)=2

2 y \frac{d y}{d x} = \frac{x}{x ^{2} - 16}, y (5) = 2

integral of sqrt(9x-36)

\int 9 x - 36 d x

(dy)/(dx)=10e^{x-y}

\frac{d y}{d x} = 10 e^{x - y}

x^{^{''}} = x

Frequently Asked Questions (FAQ)

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