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Popular >

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

Solution

derivative of

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

Solution

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}

Popular Examples

derivative of ln(e^x+1)derivative of

ln (e^{x} + 1)

integral from 1 to 4 of 3x^2-1/x

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

integral from 0 to x of sin(x)

\int_{0}^{x} sin (x) d x

(\partial)/(\partial x)(2yx^2-3)

\frac{\partial}{\partial x} (2 y x^{2} - 3)

tangent of f(x)=x^2-3x+2 tangent of

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

Frequently Asked Questions (FAQ)

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