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Popular >

derivative of x^2e^{-9x}

Solution

\frac{d}{d x} (x^{2} e^{- 9 x})

Solution

2 e^{- 9 x} x - 9 e^{- 9 x} x^{2}

Solution steps

\frac{d}{d x} (x^{2} e^{- 9 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{- 9 x}

= \frac{d}{d x} (x^{2}) e^{- 9 x} + \frac{d}{d x} (e^{- 9 x}) x^{2}

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

\frac{d}{d x} (e^{- 9 x}) = - 9 e^{- 9 x}

= 2 x e^{- 9 x} + (- 9 e^{- 9 x}) x^{2}

Simplify

= 2 e^{- 9 x} x - 9 e^{- 9 x} x^{2}

Popular Examples

(\partial)/(\partial x)((100)/(x^2+y^2+3))

\frac{\partial}{\partial x} (\frac{100}{x ^{2} + y ^{2} + 3})

integral of ((5+e^x)^2)/(e^x)

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

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n = 0 \sum \infty \frac{ln ( n )}{n}

((16)/(x(4-x^2)))^'

(\frac{16}{x ( 4 - x ^{2} )})^{^{'}}

integral of (csc^2(θ)+1)

\int (csc^{2} (θ) + 1) d θ

Frequently Asked Questions (FAQ)

What is the derivative of x^2e^{-9x} ?
The derivative of x^2e^{-9x} is 2e^{-9x}x-9e^{-9x}x^2
What is the first derivative of x^2e^{-9x} ?
The first derivative of x^2e^{-9x} is 2e^{-9x}x-9e^{-9x}x^2