What is the derivative of (3x^2-6x+6)e^{-8x} ?

The derivative of (3x^2-6x+6)e^{-8x} is -24e^{-8x}x^2+54e^{-8x}x-54e^{-8x}

What is the first derivative of (3x^2-6x+6)e^{-8x} ?

The first derivative of (3x^2-6x+6)e^{-8x} is -24e^{-8x}x^2+54e^{-8x}x-54e^{-8x}

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derivative of

(3 x^{2} - 6 x + 6) e^{- 8 x}

- 24 e^{- 8 x} x^{2} + 54 e^{- 8 x} x - 54 e^{- 8 x}

Solution steps

\frac{d}{d x} ((3 x^{2} - 6 x + 6) e^{- 8 x})

Apply the Product Rule:

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

f = 3 x^{2} - 6 x + 6, g = e^{- 8 x}

= \frac{d}{d x} (3 x^{2} - 6 x + 6) e^{- 8 x} + \frac{d}{d x} (e^{- 8 x}) (3 x^{2} - 6 x + 6)

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

\frac{d}{d x} (e^{- 8 x}) = - 8 e^{- 8 x}

= (6 x - 6) e^{- 8 x} + (- 8 e^{- 8 x}) (3 x^{2} - 6 x + 6)

Simplify

(6 x - 6) e^{- 8 x} + (- 8 e^{- 8 x}) (3 x^{2} - 6 x + 6) : - 24 e^{- 8 x} x^{2} + 54 e^{- 8 x} x - 54 e^{- 8 x}

= - 24 e^{- 8 x} x^{2} + 54 e^{- 8 x} x - 54 e^{- 8 x}

y \frac{d y}{d x} = (y^{2} - y) (2 x + 5)

a^{2} - y^{2}

(x^{2} + 9) y^{^{'}} + x y = 0

\frac{d}{d y} (x cos (y))

\int \frac{x ^{3} + x ^{2}}{x ^{2} + 5 x + 6} d x

What is the derivative of (3x^2-6x+6)e^{-8x} ?
The derivative of (3x^2-6x+6)e^{-8x} is -24e^{-8x}x^2+54e^{-8x}x-54e^{-8x}
What is the first derivative of (3x^2-6x+6)e^{-8x} ?
The first derivative of (3x^2-6x+6)e^{-8x} is -24e^{-8x}x^2+54e^{-8x}x-54e^{-8x}