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Popular >

derivative of x^5e^{-3x}

Solution

\frac{d}{d x} (x^{5} e^{- 3 x})

Solution

5 e^{- 3 x} x^{4} - 3 e^{- 3 x} x^{5}

Solution steps

\frac{d}{d x} (x^{5} e^{- 3 x})

Apply the Product Rule:

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

f = x^{5}, g = e^{- 3 x}

= \frac{d}{d x} (x^{5}) e^{- 3 x} + \frac{d}{d x} (e^{- 3 x}) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 5 x^{4} e^{- 3 x} + (- 3 e^{- 3 x}) x^{5}

Simplify

= 5 e^{- 3 x} x^{4} - 3 e^{- 3 x} x^{5}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of x^5e^{-3x} ?
The derivative of x^5e^{-3x} is 5e^{-3x}x^4-3e^{-3x}x^5
What is the first derivative of x^5e^{-3x} ?
The first derivative of x^5e^{-3x} is 5e^{-3x}x^4-3e^{-3x}x^5