en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x/(sqrt(x+1))

Solution

derivative of

\frac{x}{x + 1}

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

Popular Examples

sum from n=0 to infinity of 1/(n^3-n)

n = 0 \sum \infty \frac{1}{n ^{3} - n}

integral of 1/(x^3-4x^2+3x)

\int \frac{1}{x ^{3} - 4 x ^{2} + 3 x} d x

integral of 4x(x^2+5)^3

\int 4 x (x^{2} + 5)^{3} d x

limit as h approaches 0 of x^2+3xh

h \to 0 lim (x^{2} + 3 x h)

integral of (sqrt(y^2-16))/y

\int \frac{y ^{2} - 16}{y} d y

Frequently Asked Questions (FAQ)

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