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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Graph

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y^{''}+3y^'+2y=sin(e^x)

y^{^{''}} + 3 y^{^{'}} + 2 y = sin (e^{x})

integral from 1 to 2 of 3/(sqrt(4x-x^2))

\int_{1}^{2} \frac{3}{4 x - x ^{2}} d x

Frequently Asked Questions (FAQ)

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