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Popular >

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

Solution

\frac{d}{d x} (x^{3} \cdot 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

integral of ((x+2)/(x^2+4x))

\int (\frac{x + 2}{x ^{2} + 4 x}) d x

integral of ((7^x))/(sqrt(1-7^{2x))}

\int \frac{( 7 ^{x} )}{1 - 7 ^{2 x}} d x

derivative of cos(a^7+x^7)derivative of

cos (a^{7} + x^{7})

integral of e^{-3}

\int e^{- 3} d x

limit as x approaches pi/2 of cos(2x)

x \to \frac{π}{2} lim (cos (2 x))

Frequently Asked Questions (FAQ)

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