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)

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\frac{d}{d x} (\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}}

3 x^{2} + 4

x \to 0 lim (\frac{( e ^{x} - e ^{- x} - 2 x )}{( x - sin ( x ) )})

y = \frac{1}{arctan ( x )}

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

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

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)