What is the (x^3e^{-3x})^' ?

The (x^3e^{-3x})^' is 3e^{-3x}x^2-3e^{-3x}x^3

What is the first (x^3e^{-3x})^' ?

The first (x^3e^{-3x})^' is 3e^{-3x}x^2-3e^{-3x}x^3

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(x^{3} e^{- 3 x})^{^{'}}

3 e^{- 3 x} x^{2} - 3 e^{- 3 x} x^{3}

Solution steps

(x^{3} e^{- 3 x})^{'}

Apply the Product Rule:

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

f = x^{3}, g = e^{- 3 x}

= (x^{3})^{^{'}} e^{- 3 x} + (e^{- 3 x})^{^{'}} x^{3}

(x^{3})^{'} = 3 x^{2}

(e^{- 3 x})^{'} = - 3 e^{- 3 x}

= 3 x^{2} e^{- 3 x} + (- 3 e^{- 3 x}) x^{3}

Simplify

= 3 e^{- 3 x} x^{2} - 3 e^{- 3 x} x^{3}

y = x^{2}

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

\int_{0}^{2} 1 + \frac{5}{4 + x ^{2}} d x

x \to - 8 + lim (\frac{x + 7}{x + 8})

x \to 0 + lim (x^{x} - 1)

What is the (x^3e^{-3x})^' ?
The (x^3e^{-3x})^' is 3e^{-3x}x^2-3e^{-3x}x^3
What is the first (x^3e^{-3x})^' ?
The first (x^3e^{-3x})^' is 3e^{-3x}x^2-3e^{-3x}x^3