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Popular >

derivative of x^3e^{-4x}

Solution

\frac{d}{d x} (x^{3} e^{- 4 x})

Solution

3 e^{- 4 x} x^{2} - 4 e^{- 4 x} x^{3}

Solution steps

\frac{d}{d x} (x^{3} e^{- 4 x})

Apply the Product Rule:

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

f = x^{3}, g = e^{- 4 x}

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

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

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

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

Simplify

= 3 e^{- 4 x} x^{2} - 4 e^{- 4 x} x^{3}

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Frequently Asked Questions (FAQ)

What is the derivative of x^3e^{-4x} ?
The derivative of x^3e^{-4x} is 3e^{-4x}x^2-4e^{-4x}x^3
What is the first derivative of x^3e^{-4x} ?
The first derivative of x^3e^{-4x} is 3e^{-4x}x^2-4e^{-4x}x^3