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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

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\int sin^{2} (2 θ) d θ

y^{'''}-5y^{''}+6y^'+12y=0

y^{^{'''}} - 5 y^{^{''}} + 6 y^{^{'}} + 12 y = 0

derivative of 4/3 x^3+2

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integral from 0 to infinity of 7/(x^2+1)

\int_{0}^{\infty} \frac{7}{x ^{2} + 1} d x

Frequently Asked Questions (FAQ)

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