What is the derivative of (12x^2-24x+24)e^{-8x} ?

The derivative of (12x^2-24x+24)e^{-8x} is -96e^{-8x}x^2+216e^{-8x}x-216e^{-8x}

What is the first derivative of (12x^2-24x+24)e^{-8x} ?

The first derivative of (12x^2-24x+24)e^{-8x} is -96e^{-8x}x^2+216e^{-8x}x-216e^{-8x}

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derivative of

(12 x^{2} - 24 x + 24) e^{- 8 x}

- 96 e^{- 8 x} x^{2} + 216 e^{- 8 x} x - 216 e^{- 8 x}

Solution steps

\frac{d}{d x} ((12 x^{2} - 24 x + 24) e^{- 8 x})

Apply the Product Rule:

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

f = 12 x^{2} - 24 x + 24, g = e^{- 8 x}

= \frac{d}{d x} (12 x^{2} - 24 x + 24) e^{- 8 x} + \frac{d}{d x} (e^{- 8 x}) (12 x^{2} - 24 x + 24)

\frac{d}{d x} (12 x^{2} - 24 x + 24) = 24 x - 24

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

= (24 x - 24) e^{- 8 x} + (- 8 e^{- 8 x}) (12 x^{2} - 24 x + 24)

Simplify

(24 x - 24) e^{- 8 x} + (- 8 e^{- 8 x}) (12 x^{2} - 24 x + 24) : - 96 e^{- 8 x} x^{2} + 216 e^{- 8 x} x - 216 e^{- 8 x}

= - 96 e^{- 8 x} x^{2} + 216 e^{- 8 x} x - 216 e^{- 8 x}

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\frac{\partial}{\partial y} (2 x ln (y))

What is the derivative of (12x^2-24x+24)e^{-8x} ?
The derivative of (12x^2-24x+24)e^{-8x} is -96e^{-8x}x^2+216e^{-8x}x-216e^{-8x}
What is the first derivative of (12x^2-24x+24)e^{-8x} ?
The first derivative of (12x^2-24x+24)e^{-8x} is -96e^{-8x}x^2+216e^{-8x}x-216e^{-8x}