What is (\partial)/(\partial x)((x+3)/(x^2-x-2)) ?

The answer to (\partial)/(\partial x)((x+3)/(x^2-x-2)) is (-x^2-6x+1)/((x^2-x-2)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((x+3)/(x^2-x-2))

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{\partial}{\partial x} (x + 3) = 1

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

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

Simplify

\frac{1 \cdot ( x ^{2} - x - 2 ) - ( 2 x - 1 ) ( x + 3 )}{( x ^{2} - x - 2 ) ^{2}} : \frac{- x ^{2} - 6 x + 1}{( x ^{2} - x - 2 ) ^{2}}

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

x \to 0 lim (ln (sin (2 x)))

\int_{0}^{\frac{π}{4}} tan^{3} (x) sec^{\frac{5}{2}} (x) d x

\int \frac{x + 6}{x ^{2} + 16} d x

\int \frac{8 x ^{4} - 4 x ^{3} - 7 x}{x} d x

\int \frac{1}{sin ^{2} ( a x )} d x

What is (\partial)/(\partial x)((x+3)/(x^2-x-2)) ?
The answer to (\partial)/(\partial x)((x+3)/(x^2-x-2)) is (-x^2-6x+1)/((x^2-x-2)^2)