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

The derivative of (-2x^2+2x+3(-x^2-3x-4)) is 8x^3+12x^2-2x-17

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

The first derivative of (-2x^2+2x+3(-x^2-3x-4)) is 8x^3+12x^2-2x-17

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

8 x^{3} + 12 x^{2} - 2 x - 17

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = - 2 x^{2} + 2 x + 3, g = - x^{2} - 3 x - 4

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

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

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

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

Simplify

(- 4 x + 2) (- x^{2} - 3 x - 4) + (- 2 x - 3) (- 2 x^{2} + 2 x + 3) : 8 x^{3} + 12 x^{2} - 2 x - 17

= 8 x^{3} + 12 x^{2} - 2 x - 17

\frac{d}{d x} (\frac{d y}{d x}) + 81 y = 0

\int cos (\frac{u}{v}) d u

x \to + 0 lim (\frac{sin ( 0 )}{0})

\int 6 t^{4} e^{- t^{5}} d t

4 e^{(\frac{2 t}{3})}

What is the derivative of (-2x^2+2x+3(-x^2-3x-4)) ?
The derivative of (-2x^2+2x+3(-x^2-3x-4)) is 8x^3+12x^2-2x-17
What is the first derivative of (-2x^2+2x+3(-x^2-3x-4)) ?
The first derivative of (-2x^2+2x+3(-x^2-3x-4)) is 8x^3+12x^2-2x-17