What is the derivative of y=x^2e^{-3x} ?

The derivative of y=x^2e^{-3x} is 2e^{-3x}x-3e^{-3x}x^2

What is the first derivative of y=x^2e^{-3x} ?

The first derivative of y=x^2e^{-3x} is 2e^{-3x}x-3e^{-3x}x^2

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derivative of

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

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

Solution steps

\frac{d}{d x} (x^{2} e^{- 3 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{- 3 x}

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

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

\frac{d}{d x} (e^{- 3 x}) = - 3 e^{- 3 x}

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

Simplify

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

\int \frac{s}{3 s ^{2} + 1} d s

\frac{d}{d x} (\frac{e ^{2 x + 1}}{2 x + 5})

n = 1 \sum \infty \frac{ln ( n )}{2 n}

y = \frac{3}{x}, y = 12 x

\frac{\partial}{\partial x} (y^{\frac{z}{x}})

What is the derivative of y=x^2e^{-3x} ?
The derivative of y=x^2e^{-3x} is 2e^{-3x}x-3e^{-3x}x^2
What is the first derivative of y=x^2e^{-3x} ?
The first derivative of y=x^2e^{-3x} is 2e^{-3x}x-3e^{-3x}x^2