en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln|1+x|

Solution

\frac{d}{d x} (ln ∣ 1 + x ∣)

Solution

\frac{1}{1 + x}

Solution steps

\frac{d}{d x} (ln ∣ 1 + x ∣)

Apply the chain rule:

\frac{1}{∣ 1 + x ∣} \frac{d}{d x} (∣ 1 + x ∣)

= \frac{1}{∣ 1 + x ∣} \frac{d}{d x} (∣ 1 + x ∣)

\frac{d}{d x} (∣ 1 + x ∣) = \frac{1 + x}{∣ 1 + x ∣}

= \frac{1}{∣ 1 + x ∣} \cdot \frac{1 + x}{∣ 1 + x ∣}

Simplify

\frac{1}{∣ 1 + x ∣} \cdot \frac{1 + x}{∣ 1 + x ∣} : \frac{1}{1 + x}

= \frac{1}{1 + x}

Graph

Popular Examples

derivative of arcsec(x)-8x derivative of

arcsec (x) - 8 x

tangent of sin(x),\at x=(-pi/3)tangent of

sin (x), at x = (- \frac{π}{3})

integral from 0 to pi/5 of xsin(10x)

\int_{0}^{\frac{π}{5}} x sin (10 x) d x

integral of \sqrt[7]{x}+1/(\sqrt[7]{x)}

\int 7 x + \frac{1}{7 x} d x

integral from 0 to sqrt(t of)xe^{-x^2}

\int_{0}^{t} x e^{- x^{2}} d x

Frequently Asked Questions (FAQ)

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