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

The derivative of x^2*e^{-4x} is 2e^{-4x}x-4e^{-4x}x^2

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

The first derivative of x^2*e^{-4x} is 2e^{-4x}x-4e^{-4x}x^2

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

2 e^{- 4 x} x - 4 e^{- 4 x} x^{2}

Solution steps

\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}

= \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}

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

Simplify

= 2 e^{- 4 x} x - 4 e^{- 4 x} x^{2}

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\int \frac{ln ( z )}{z ^{2}} d z

\int_{- 1}^{3} \frac{4 x ^{2} - 7}{2 x + 3} d x

\frac{d}{d x} (I n)

\frac{d y}{d x} = 12 x^{3} y

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