What is the derivative of (x^2+2x-5/((x+1)^2)) ?

The derivative of (x^2+2x-5/((x+1)^2)) is (12)/((x+1)^3)

What is the first derivative of (x^2+2x-5/((x+1)^2)) ?

The first derivative of (x^2+2x-5/((x+1)^2)) is (12)/((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 - 5}{( x + 1 ) ^{2}})

\frac{12}{( x + 1 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 2 x - 5}{( 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 - 5 ) ( x + 1 ) ^{2} - \frac{d}{d x} ( ( x + 1 ) ^{2} ) ( x ^{2} + 2 x - 5 )}{( ( x + 1 ) ^{2} ) ^{2}}

\frac{d}{d x} (x^{2} + 2 x - 5) = 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 - 5 )}{( ( x + 1 ) ^{2} ) ^{2}}

Simplify

\frac{( 2 x + 2 ) ( x + 1 ) ^{2} - 2 ( x + 1 ) ( x ^{2} + 2 x - 5 )}{( ( x + 1 ) ^{2} ) ^{2}} : \frac{12}{( x + 1 ) ^{3}}

= \frac{12}{( x + 1 ) ^{3}}

\int_{0}^{2} 2 x e^{x^{2}} d x

\int \frac{3}{x} + 3 x d x

\frac{\partial}{\partial t} (t e^{t})

x = 4 y, x = y^{2} - 12

3 x^{- 4}

What is the derivative of (x^2+2x-5/((x+1)^2)) ?
The derivative of (x^2+2x-5/((x+1)^2)) is (12)/((x+1)^3)
What is the first derivative of (x^2+2x-5/((x+1)^2)) ?
The first derivative of (x^2+2x-5/((x+1)^2)) is (12)/((x+1)^3)