What is the derivative of y=(6x^2-12x+12)e^{-8x} ?

The derivative of y=(6x^2-12x+12)e^{-8x} is -48e^{-8x}x^2+108e^{-8x}x-108e^{-8x}

What is the first derivative of y=(6x^2-12x+12)e^{-8x} ?

The first derivative of y=(6x^2-12x+12)e^{-8x} is -48e^{-8x}x^2+108e^{-8x}x-108e^{-8x}

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derivative of

y = (6 x^{2} - 12 x + 12) e^{- 8 x}

- 48 e^{- 8 x} x^{2} + 108 e^{- 8 x} x - 108 e^{- 8 x}

Solution steps

\frac{d}{d x} ((6 x^{2} - 12 x + 12) e^{- 8 x})

Apply the Product Rule:

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

f = 6 x^{2} - 12 x + 12, g = e^{- 8 x}

= \frac{d}{d x} (6 x^{2} - 12 x + 12) e^{- 8 x} + \frac{d}{d x} (e^{- 8 x}) (6 x^{2} - 12 x + 12)

\frac{d}{d x} (6 x^{2} - 12 x + 12) = 12 x - 12

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

= (12 x - 12) e^{- 8 x} + (- 8 e^{- 8 x}) (6 x^{2} - 12 x + 12)

Simplify

(12 x - 12) e^{- 8 x} + (- 8 e^{- 8 x}) (6 x^{2} - 12 x + 12) : - 48 e^{- 8 x} x^{2} + 108 e^{- 8 x} x - 108 e^{- 8 x}

= - 48 e^{- 8 x} x^{2} + 108 e^{- 8 x} x - 108 e^{- 8 x}

\frac{d ^{2}}{d x ^{2}} (x^{2} + 1)

2 x^{2} + 3 x - 4

\frac{d}{d x} (ln (π x))

\int \frac{5}{( x + 1 ) ^{2}} d x

f (t) = t 4 - t^{2}

What is the derivative of y=(6x^2-12x+12)e^{-8x} ?
The derivative of y=(6x^2-12x+12)e^{-8x} is -48e^{-8x}x^2+108e^{-8x}x-108e^{-8x}
What is the first derivative of y=(6x^2-12x+12)e^{-8x} ?
The first derivative of y=(6x^2-12x+12)e^{-8x} is -48e^{-8x}x^2+108e^{-8x}x-108e^{-8x}