What is the derivative of (x^2-3x+2)/(-x^2-4x+4) ?

The derivative of (x^2-3x+2)/(-x^2-4x+4) is (-7x^2+12x-4)/((-x^2-4x+4)^2)

What is the first derivative of (x^2-3x+2)/(-x^2-4x+4) ?

The first derivative of (x^2-3x+2)/(-x^2-4x+4) is (-7x^2+12x-4)/((-x^2-4x+4)^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 ^{2} - 3 x + 2}{- x ^{2} - 4 x + 4}

\frac{- 7 x ^{2} + 12 x - 4}{( - x ^{2} - 4 x + 4 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

(2 x - 3) (- x^{2} - 4 x + 4) - (- 2 x - 4) (x^{2} - 3 x + 2) : - 7 x^{2} + 12 x - 4

= \frac{- 7 x ^{2} + 12 x - 4}{( - x ^{2} - 4 x + 4 ) ^{2}}

\frac{\partial}{\partial x} (y^{4} sin (5 x))

\frac{1}{s ^{2} + 9}

\frac{\partial}{\partial y} (\frac{y}{x + y})

f (x) = (14 x - x^{2})^{3}

What is the derivative of (x^2-3x+2)/(-x^2-4x+4) ?
The derivative of (x^2-3x+2)/(-x^2-4x+4) is (-7x^2+12x-4)/((-x^2-4x+4)^2)
What is the first derivative of (x^2-3x+2)/(-x^2-4x+4) ?
The first derivative of (x^2-3x+2)/(-x^2-4x+4) is (-7x^2+12x-4)/((-x^2-4x+4)^2)