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)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\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}}

\frac{5}{x + 1}

\frac{d}{d x} (sec (x))

\int_{1}^{2} 11 e^{\frac{1}{x}} d x

lo g_{4} (e^{- x} cos (π x))

\int 4 cos (θ) sin (θ) d θ

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)