What is the derivative of f(x)=x^3e^{-2x} ?

The derivative of f(x)=x^3e^{-2x} is 3e^{-2x}x^2-2e^{-2x}x^3

What is the first derivative of f(x)=x^3e^{-2x} ?

The first derivative of f(x)=x^3e^{-2x} is 3e^{-2x}x^2-2e^{-2x}x^3

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derivative of

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

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

Solution steps

\frac{d}{d x} (x^{3} e^{- 2 x})

Apply the Product Rule:

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

f = x^{3}, g = e^{- 2 x}

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

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

\frac{d}{d x} (e^{- 2 x}) = - 2 e^{- 2 x}

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

Simplify

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

2 π r^{2}

y = (x - 2)^{4 x}

\int \frac{x ^{3} + 3 x ^{2} - 2 x + 1}{x ^{4} + 5 x ^{2} + 4} d x

\frac{d}{d x} \frac{( x ^{2} - 1 ) ^{\frac{3}{2}}}{3 x ^{3}}

x \to 9 + lim (\frac{2}{x - 9})

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