en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

((x^2)/(x^2-x-2))^'

Solution

(\frac{x ^{2}}{x ^{2} - x - 2})^{^{'}}

Solution

\frac{- x ^{2} - 4 x}{( x ^{2} - x - 2 ) ^{2}}

Solution steps

(\frac{x ^{2}}{x ^{2} - x - 2})^{'}

Apply the Quotient Rule:

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

= \frac{( x ^{2} ) ^{^{'}} ( x ^{2} - x - 2 ) - ( x ^{2} - x - 2 ) ^{^{'}} x ^{2}}{( x ^{2} - x - 2 ) ^{2}}

(x^{2})^{'} = 2 x

(x^{2} - x - 2)^{'} = 2 x - 1

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

Expand

2 x (x^{2} - x - 2) - (2 x - 1) x^{2} : - x^{2} - 4 x

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

Popular Examples

inverse oflaplace (2s-3)/((s+4)(s-3)^3)inverse laplace

\frac{2 s - 3}{( s + 4 ) ( s - 3 ) ^{3}}

integral of (15x^4)/(x^5+7)

\int \frac{15 x ^{4}}{x ^{5} + 7} d x

(\partial)/(\partial x)(-2ysin(x))

\frac{\partial}{\partial x} (- 2 y sin (x))

integral of (sin(20t))/(sin(10t))

\int \frac{sin ( 20 t )}{sin ( 10 t )} d x

integral of (3t+8)^{2.8}

\int (3 t + 8)^{2.8} d t

Frequently Asked Questions (FAQ)

What is the ((x^2)/(x^2-x-2))^' ?
The ((x^2)/(x^2-x-2))^' is (-x^2-4x)/((x^2-x-2)^2)
What is the first ((x^2)/(x^2-x-2))^' ?
The first ((x^2)/(x^2-x-2))^' is (-x^2-4x)/((x^2-x-2)^2)