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

The derivative of x^3e^{-2x} is 3e^{-2x}x^2-2e^{-2x}x^3

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

The first derivative of x^3e^{-2x} is 3e^{-2x}x^2-2e^{-2x}x^3

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derivative of

x^{3} e^{- 2 x}

3 e^{- 2 x} x^{2} - 2 e^{- 2 x} x^{3}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

= 3 e^{- 2 x} x^{2} - 2 e^{- 2 x} x^{3}

What is the derivative of x^3e^{-2x} ?
The derivative of x^3e^{-2x} is 3e^{-2x}x^2-2e^{-2x}x^3
What is the first derivative of x^3e^{-2x} ?
The first derivative of x^3e^{-2x} is 3e^{-2x}x^2-2e^{-2x}x^3