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

The derivative of (2x/((1+x)^2)) is (2(1-x))/((1+x)^3)

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

The first derivative of (2x/((1+x)^2)) is (2(1-x))/((1+x)^3)

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

\frac{2 ( 1 - x )}{( 1 + x ) ^{3}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

2 \cdot \frac{1 \cdot ( 1 + x ) ^{2} - 2 ( 1 + x ) x}{( ( 1 + x ) ^{2} ) ^{2}} : \frac{2 ( 1 - x )}{( 1 + x ) ^{3}}

= \frac{2 ( 1 - x )}{( 1 + x ) ^{3}}

\int \frac{ln ( 3 x )}{x} d x

- \frac{18}{t ^{3}} + \frac{3}{t ^{2}}

\int x x + 2 d x

\int (x - 1) ln (x) d x

\frac{\partial}{\partial x} (- f (r, x) r sin (x) \cdot sin (x))

What is the derivative of (2x/((1+x)^2)) ?
The derivative of (2x/((1+x)^2)) is (2(1-x))/((1+x)^3)
What is the first derivative of (2x/((1+x)^2)) ?
The first derivative of (2x/((1+x)^2)) is (2(1-x))/((1+x)^3)