What is the derivative of y=x^2e^{-x} ?

The derivative of y=x^2e^{-x} is 2e^{-x}x-e^{-x}x^2

What is the first derivative of y=x^2e^{-x} ?

The first derivative of y=x^2e^{-x} is 2e^{-x}x-e^{-x}x^2

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

\frac{d y}{d x} + \frac{y}{x + 2} = 5 (x - 2) y^{\frac{1}{2}}

y = 4 x - 3 x^{2}

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

n = 1 \sum \infty \frac{2}{π ^{n}}

\int \frac{x ^{5}}{5} d x

What is the derivative of y=x^2e^{-x} ?
The derivative of y=x^2e^{-x} is 2e^{-x}x-e^{-x}x^2
What is the first derivative of y=x^2e^{-x} ?
The first derivative of y=x^2e^{-x} is 2e^{-x}x-e^{-x}x^2