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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (2 x + 2 x^{2}) = 2 + 4 x

\frac{d}{d x} ((1 + 2 x)^{2}) = 4 (1 + 2 x)

= \frac{( 2 + 4 x ) ( 1 + 2 x ) ^{2} - 4 ( 1 + 2 x ) ( 2 x + 2 x ^{2} )}{( ( 1 + 2 x ) ^{2} ) ^{2}}

Simplify

\frac{( 2 + 4 x ) ( 1 + 2 x ) ^{2} - 4 ( 1 + 2 x ) ( 2 x + 2 x ^{2} )}{( ( 1 + 2 x ) ^{2} ) ^{2}} : \frac{2}{( 1 + 2 x ) ^{3}}

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

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