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

The derivative of (x^2+2x-3/((x+1)^2)) is 8/((x+1)^3)

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

The first derivative of (x^2+2x-3/((x+1)^2)) is 8/((x+1)^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{x ^{2} + 2 x - 3}{( x + 1 ) ^{2}})

\frac{8}{( x + 1 ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( 2 x + 2 ) ( x + 1 ) ^{2} - 2 ( x + 1 ) ( x ^{2} + 2 x - 3 )}{( ( x + 1 ) ^{2} ) ^{2}} : \frac{8}{( x + 1 ) ^{3}}

= \frac{8}{( x + 1 ) ^{3}}

x \to - 4 lim (\frac{x ^{2} - 6}{4 - x})

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

\int y y d y

\frac{d y}{d x} = x (5 - y)

x \to \infty lim (\frac{3}{x})

What is the derivative of (x^2+2x-3/((x+1)^2)) ?
The derivative of (x^2+2x-3/((x+1)^2)) is 8/((x+1)^3)
What is the first derivative of (x^2+2x-3/((x+1)^2)) ?
The first derivative of (x^2+2x-3/((x+1)^2)) is 8/((x+1)^3)