What is the derivative of y=(9x^2-18x+18)e^{-4x} ?

The derivative of y=(9x^2-18x+18)e^{-4x} is -36e^{-4x}x^2+90e^{-4x}x-90e^{-4x}

What is the first derivative of y=(9x^2-18x+18)e^{-4x} ?

The first derivative of y=(9x^2-18x+18)e^{-4x} is -36e^{-4x}x^2+90e^{-4x}x-90e^{-4x}

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derivative of

y = (9 x^{2} - 18 x + 18) e^{- 4 x}

- 36 e^{- 4 x} x^{2} + 90 e^{- 4 x} x - 90 e^{- 4 x}

Solution steps

\frac{d}{d x} ((9 x^{2} - 18 x + 18) e^{- 4 x})

Apply the Product Rule:

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

f = 9 x^{2} - 18 x + 18, g = e^{- 4 x}

= \frac{d}{d x} (9 x^{2} - 18 x + 18) e^{- 4 x} + \frac{d}{d x} (e^{- 4 x}) (9 x^{2} - 18 x + 18)

\frac{d}{d x} (9 x^{2} - 18 x + 18) = 18 x - 18

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

= (18 x - 18) e^{- 4 x} + (- 4 e^{- 4 x}) (9 x^{2} - 18 x + 18)

Simplify

(18 x - 18) e^{- 4 x} + (- 4 e^{- 4 x}) (9 x^{2} - 18 x + 18) : - 36 e^{- 4 x} x^{2} + 90 e^{- 4 x} x - 90 e^{- 4 x}

= - 36 e^{- 4 x} x^{2} + 90 e^{- 4 x} x - 90 e^{- 4 x}

What is the derivative of y=(9x^2-18x+18)e^{-4x} ?
The derivative of y=(9x^2-18x+18)e^{-4x} is -36e^{-4x}x^2+90e^{-4x}x-90e^{-4x}
What is the first derivative of y=(9x^2-18x+18)e^{-4x} ?
The first derivative of y=(9x^2-18x+18)e^{-4x} is -36e^{-4x}x^2+90e^{-4x}x-90e^{-4x}