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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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