en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial x)(x^{1/y})

\frac{\partial}{\partial x} (x^{\frac{1}{y}})

integral of 1/(5xlog_{7)(x)}

\int \frac{1}{5 x lo g _{7} ( x )} d x

limit as x approaches 6-of f(x)

x \to 6 - lim (f (x))

(\partial ^2)/(\partial x\partial y)(3xye^{-x^2y})

\frac{\partial ^{2}}{\partial x \partial y} (3 x y e^{- x^{2} y})

(\partial)/(\partial x)(x/(6+y))

\frac{\partial}{\partial x} (\frac{x}{6 + y})

Frequently Asked Questions (FAQ)

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