en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

derivative of (x^2/((1+x)))

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Graph

Popular Examples

limit as x approaches-4 of-7

x \to - 4 lim (- 7)

laplacetransform 6e^{-2t}

l a pl a ce t r an s f or m 6 e^{- 2 t}

d/(dy)(ln(cos(x/(y^2))))

\frac{d}{d y} (ln (cos (\frac{x}{y ^{2}})))

slope of (3/10 ,-1/2),(1/5 , 1/5)

s l o p e (\frac{3}{10}, - \frac{1}{2}), (\frac{1}{5}, \frac{1}{5})

(\partial)/(\partial x)(y^3sin(5x))

\frac{\partial}{\partial x} (y^{3} sin (5 x))

Frequently Asked Questions (FAQ)

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