What is the derivative of x^2e^{-5x} ?

The derivative of x^2e^{-5x} is 2e^{-5x}x-5e^{-5x}x^2

What is the first derivative of x^2e^{-5x} ?

The first derivative of x^2e^{-5x} is 2e^{-5x}x-5e^{-5x}x^2

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derivative of

x^{2} e^{- 5 x}

2 e^{- 5 x} x - 5 e^{- 5 x} x^{2}

Solution steps

\frac{d}{d x} (x^{2} e^{- 5 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{- 5 x}

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

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

\frac{d}{d x} (e^{- 5 x}) = - 5 e^{- 5 x}

= 2 x e^{- 5 x} + (- 5 e^{- 5 x}) x^{2}

Simplify

= 2 e^{- 5 x} x - 5 e^{- 5 x} x^{2}

\int_{\frac{1}{3}}^{5} 6 x ln (3 x) d x

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

ln (x), at 1

\frac{d}{d x} ((4 x + 1) (1 - x)^{3})

\int \frac{x x}{x ^{2}} d x

What is the derivative of x^2e^{-5x} ?
The derivative of x^2e^{-5x} is 2e^{-5x}x-5e^{-5x}x^2
What is the first derivative of x^2e^{-5x} ?
The first derivative of x^2e^{-5x} is 2e^{-5x}x-5e^{-5x}x^2