What is the derivative of (10x^2-20x+20)e^{-6x} ?

The derivative of (10x^2-20x+20)e^{-6x} is -60e^{-6x}x^2+140e^{-6x}x-140e^{-6x}

What is the first derivative of (10x^2-20x+20)e^{-6x} ?

The first derivative of (10x^2-20x+20)e^{-6x} is -60e^{-6x}x^2+140e^{-6x}x-140e^{-6x}

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derivative of

(10 x^{2} - 20 x + 20) e^{- 6 x}

- 60 e^{- 6 x} x^{2} + 140 e^{- 6 x} x - 140 e^{- 6 x}

Solution steps

\frac{d}{d x} ((10 x^{2} - 20 x + 20) e^{- 6 x})

Apply the Product Rule:

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

f = 10 x^{2} - 20 x + 20, g = e^{- 6 x}

= \frac{d}{d x} (10 x^{2} - 20 x + 20) e^{- 6 x} + \frac{d}{d x} (e^{- 6 x}) (10 x^{2} - 20 x + 20)

\frac{d}{d x} (10 x^{2} - 20 x + 20) = 20 x - 20

\frac{d}{d x} (e^{- 6 x}) = - 6 e^{- 6 x}

= (20 x - 20) e^{- 6 x} + (- 6 e^{- 6 x}) (10 x^{2} - 20 x + 20)

Simplify

(20 x - 20) e^{- 6 x} + (- 6 e^{- 6 x}) (10 x^{2} - 20 x + 20) : - 60 e^{- 6 x} x^{2} + 140 e^{- 6 x} x - 140 e^{- 6 x}

= - 60 e^{- 6 x} x^{2} + 140 e^{- 6 x} x - 140 e^{- 6 x}

\int \frac{( sin ^{3} ( x ) )}{cos ( x )} d x

\frac{d}{d x} (4 x^{3} + 3 x)

\int_{- 1}^{7} (2 x + 7) - (x^{2} - 4 x) d x

\int \frac{1}{- csc ( y )} d y

f (x) = - \frac{x + 3 arcsin ( x )}{4}

What is the derivative of (10x^2-20x+20)e^{-6x} ?
The derivative of (10x^2-20x+20)e^{-6x} is -60e^{-6x}x^2+140e^{-6x}x-140e^{-6x}
What is the first derivative of (10x^2-20x+20)e^{-6x} ?
The first derivative of (10x^2-20x+20)e^{-6x} is -60e^{-6x}x^2+140e^{-6x}x-140e^{-6x}