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

The derivative of (2x^2+x-3/(-3x^2-4x+2)) is (-5x^2-10x-10)/((-3x^2-4x+2)^2)

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

The first derivative of (2x^2+x-3/(-3x^2-4x+2)) is (-5x^2-10x-10)/((-3x^2-4x+2)^2)

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

\frac{- 5 x ^{2} - 10 x - 10}{( - 3 x ^{2} - 4 x + 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (2 x^{2} + x - 3) = 4 x + 1

\frac{d}{d x} (- 3 x^{2} - 4 x + 2) = - 6 x - 4

= \frac{( 4 x + 1 ) ( - 3 x ^{2} - 4 x + 2 ) - ( - 6 x - 4 ) ( 2 x ^{2} + x - 3 )}{( - 3 x ^{2} - 4 x + 2 ) ^{2}}

Expand

(4 x + 1) (- 3 x^{2} - 4 x + 2) - (- 6 x - 4) (2 x^{2} + x - 3) : - 5 x^{2} - 10 x - 10

= \frac{- 5 x ^{2} - 10 x - 10}{( - 3 x ^{2} - 4 x + 2 ) ^{2}}

x \to 2 lim (16)

n = 1 \sum \infty 5 (4)^{n - 1}

cos (3 x)

\frac{d}{d x} (\frac{1.05}{1 + 100 e ^{- 0.285 x}})

\int_{0}^{1.2} 1 - \frac{y}{2} d y

What is the derivative of (2x^2+x-3/(-3x^2-4x+2)) ?
The derivative of (2x^2+x-3/(-3x^2-4x+2)) is (-5x^2-10x-10)/((-3x^2-4x+2)^2)
What is the first derivative of (2x^2+x-3/(-3x^2-4x+2)) ?
The first derivative of (2x^2+x-3/(-3x^2-4x+2)) is (-5x^2-10x-10)/((-3x^2-4x+2)^2)