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

The derivative of ((x+1)^2)/((x-1)(x+2)) is (-x^2-6x-5)/((x-1)^2(x+2)^2)

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

The first derivative of ((x+1)^2)/((x-1)(x+2)) is (-x^2-6x-5)/((x-1)^2(x+2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

\frac{- x ^{2} - 6 x - 5}{( x - 1 ) ^{2} ( x + 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 ( x + 1 ) ( x - 1 ) ( x + 2 ) - ( 2 x + 1 ) ( x + 1 ) ^{2}}{( ( x - 1 ) ( x + 2 ) ) ^{2}} : \frac{- x ^{2} - 6 x - 5}{( x - 1 ) ^{2} ( x + 2 ) ^{2}}

= \frac{- x ^{2} - 6 x - 5}{( x - 1 ) ^{2} ( x + 2 ) ^{2}}

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

\int 10 x^{- \frac{1}{2}} + 1 d x

2 \frac{1}{x}, at x = 3

\int \frac{9 x ^{2} - 1}{x} d x

\int (1 - 2 e^{t a n (x)}) sec^{2} (x) d x

What is the derivative of ((x+1)^2)/((x-1)(x+2)) ?
The derivative of ((x+1)^2)/((x-1)(x+2)) is (-x^2-6x-5)/((x-1)^2(x+2)^2)
What is the first derivative of ((x+1)^2)/((x-1)(x+2)) ?
The first derivative of ((x+1)^2)/((x-1)(x+2)) is (-x^2-6x-5)/((x-1)^2(x+2)^2)