What is the derivative of ax^2e^{-4x} ?

The derivative of ax^2e^{-4x} is a(2e^{-4x}x-4e^{-4x}x^2)

What is the first derivative of ax^2e^{-4x} ?

The first derivative of ax^2e^{-4x} is a(2e^{-4x}x-4e^{-4x}x^2)

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\frac{d}{d x} (a x^{2} e^{- 4 x})

a (2 e^{- 4 x} x - 4 e^{- 4 x} x^{2})

Solution steps

\frac{d}{d x} (a x^{2} e^{- 4 x})

Take the constant out:

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

= a \frac{d}{d x} (x^{2} e^{- 4 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{- 4 x}

= a (\frac{d}{d x} (x^{2}) e^{- 4 x} + \frac{d}{d x} (e^{- 4 x}) x^{2})

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

\frac{d}{d x} (e^{- 4 x}) = - 4 e^{- 4 x}

= a (2 x e^{- 4 x} + (- 4 e^{- 4 x}) x^{2})

Simplify

= a (2 e^{- 4 x} x - 4 e^{- 4 x} x^{2})

\frac{3 d y}{d x} + 12 y = 4

\frac{\partial}{\partial x} (7 x^{2 y})

\frac{d}{d x} (- 24 + 20 x - 10 x^{3} + x^{5})

\frac{d}{d t} (t^{2} sin (t))

e^{t} - π

What is the derivative of ax^2e^{-4x} ?
The derivative of ax^2e^{-4x} is a(2e^{-4x}x-4e^{-4x}x^2)
What is the first derivative of ax^2e^{-4x} ?
The first derivative of ax^2e^{-4x} is a(2e^{-4x}x-4e^{-4x}x^2)