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

The derivative of ax^2e^{-x} is a(2e^{-x}x-e^{-x}x^2)

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

The first derivative of ax^2e^{-x} is a(2e^{-x}x-e^{-x}x^2)

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

a (2 e^{- x} x - e^{- x} x^{2})

Solution steps

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

Take the constant out:

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

= a \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}

= a (\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}

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

Simplify

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

\frac{d}{d x} (ln (\frac{3}{x ^{2} + 9}))

f (x) = x^{x}, at x = 2

(x y^{2} - x) d x + (x^{2} y + y) d y = 0

\frac{\partial}{\partial x} (20 - 2 x + 1.5 - x + 3 x)

\frac{d ^{2}}{d x ^{2}} (- 8 sin (\frac{3 x}{2} + 1))

What is the derivative of ax^2e^{-x} ?
The derivative of ax^2e^{-x} is a(2e^{-x}x-e^{-x}x^2)
What is the first derivative of ax^2e^{-x} ?
The first derivative of ax^2e^{-x} is a(2e^{-x}x-e^{-x}x^2)