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

The derivative of e^{-2x}x^3(-x+2) is 2e^{-2x}x^4-8e^{-2x}x^3+6e^{-2x}x^2

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

The first derivative of e^{-2x}x^3(-x+2) is 2e^{-2x}x^4-8e^{-2x}x^3+6e^{-2x}x^2

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derivative of

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

2 e^{- 2 x} x^{4} - 8 e^{- 2 x} x^{3} + 6 e^{- 2 x} x^{2}

Solution steps

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

Apply the Product Rule:

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

f = e^{- 2 x}, g = x^{3} (- x + 2)

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

\frac{d}{d x} (e^{- 2 x}) = - 2 e^{- 2 x}

\frac{d}{d x} (x^{3} (- x + 2)) = - 4 x^{3} + 6 x^{2}

= (- 2 e^{- 2 x}) x^{3} (- x + 2) + (- 4 x^{3} + 6 x^{2}) e^{- 2 x}

Simplify

(- 2 e^{- 2 x}) x^{3} (- x + 2) + (- 4 x^{3} + 6 x^{2}) e^{- 2 x} : 2 e^{- 2 x} x^{4} - 8 e^{- 2 x} x^{3} + 6 e^{- 2 x} x^{2}

= 2 e^{- 2 x} x^{4} - 8 e^{- 2 x} x^{3} + 6 e^{- 2 x} x^{2}

What is the derivative of e^{-2x}x^3(-x+2) ?
The derivative of e^{-2x}x^3(-x+2) is 2e^{-2x}x^4-8e^{-2x}x^3+6e^{-2x}x^2
What is the first derivative of e^{-2x}x^3(-x+2) ?
The first derivative of e^{-2x}x^3(-x+2) is 2e^{-2x}x^4-8e^{-2x}x^3+6e^{-2x}x^2