What is the derivative of 1/2 x^2e^{-2x} ?

The derivative of 1/2 x^2e^{-2x} is e^{-2x}x(-x+1)

What is the first derivative of 1/2 x^2e^{-2x} ?

The first derivative of 1/2 x^2e^{-2x} is e^{-2x}x(-x+1)

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

e^{- 2 x} x (- x + 1)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

= \frac{1}{2} (\frac{d}{d x} (x^{2}) e^{- 2 x} + \frac{d}{d x} (e^{- 2 x}) x^{2})

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

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

= \frac{1}{2} (2 x e^{- 2 x} + (- 2 e^{- 2 x}) x^{2})

Simplify

\frac{1}{2} (2 x e^{- 2 x} + (- 2 e^{- 2 x}) x^{2}) : e^{- 2 x} x (- x + 1)

= e^{- 2 x} x (- x + 1)

\frac{2 x + 9}{x}

\int \frac{y ^{3}}{( 1 - 2 y ^{4} ) ^{5}} d y

\int_{0}^{1} \frac{36}{x ^{2} - 36} d x

x \to 3 lim (\frac{x - 3}{x + 4})

n = 1 \sum \infty \frac{3 n}{5 n - 1}

What is the derivative of 1/2 x^2e^{-2x} ?
The derivative of 1/2 x^2e^{-2x} is e^{-2x}x(-x+1)
What is the first derivative of 1/2 x^2e^{-2x} ?
The first derivative of 1/2 x^2e^{-2x} is e^{-2x}x(-x+1)