What is the derivative of (3x^2-6x+6)e^{-5x} ?

The derivative of (3x^2-6x+6)e^{-5x} is -15e^{-5x}x^2+36e^{-5x}x-36e^{-5x}

What is the first derivative of (3x^2-6x+6)e^{-5x} ?

The first derivative of (3x^2-6x+6)e^{-5x} is -15e^{-5x}x^2+36e^{-5x}x-36e^{-5x}

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derivative of

(3 x^{2} - 6 x + 6) e^{- 5 x}

- 15 e^{- 5 x} x^{2} + 36 e^{- 5 x} x - 36 e^{- 5 x}

Solution steps

\frac{d}{d x} ((3 x^{2} - 6 x + 6) e^{- 5 x})

Apply the Product Rule:

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

f = 3 x^{2} - 6 x + 6, g = e^{- 5 x}

= \frac{d}{d x} (3 x^{2} - 6 x + 6) e^{- 5 x} + \frac{d}{d x} (e^{- 5 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^{- 5 x}) = - 5 e^{- 5 x}

= (6 x - 6) e^{- 5 x} + (- 5 e^{- 5 x}) (3 x^{2} - 6 x + 6)

Simplify

(6 x - 6) e^{- 5 x} + (- 5 e^{- 5 x}) (3 x^{2} - 6 x + 6) : - 15 e^{- 5 x} x^{2} + 36 e^{- 5 x} x - 36 e^{- 5 x}

= - 15 e^{- 5 x} x^{2} + 36 e^{- 5 x} x - 36 e^{- 5 x}

What is the derivative of (3x^2-6x+6)e^{-5x} ?
The derivative of (3x^2-6x+6)e^{-5x} is -15e^{-5x}x^2+36e^{-5x}x-36e^{-5x}
What is the first derivative of (3x^2-6x+6)e^{-5x} ?
The first derivative of (3x^2-6x+6)e^{-5x} is -15e^{-5x}x^2+36e^{-5x}x-36e^{-5x}