What is the derivative of (x^2-x)*e^{-x} ?

The derivative of (x^2-x)*e^{-x} is -e^{-x}x^2+3e^{-x}x-e^{-x}

What is the first derivative of (x^2-x)*e^{-x} ?

The first derivative of (x^2-x)*e^{-x} is -e^{-x}x^2+3e^{-x}x-e^{-x}

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derivative of

(x^{2} - x) \cdot e^{- x}

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= (2 x - 1) e^{- x} + (- e^{- x}) (x^{2} - x)

Simplify

(2 x - 1) e^{- x} + (- e^{- x}) (x^{2} - x) : - e^{- x} x^{2} + 3 e^{- x} x - e^{- x}

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

\int \frac{2 x + 4}{x ^{3} - 2 x ^{2}} d x

\int π cos (n x) d x

\int_{0}^{1} 6 e^{- 6 x} d x

\frac{\partial}{\partial x} (\frac{1}{2} ln (x))

x + 3 y = 35, x + 5 = y^{2}

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