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

The derivative of 2e^{-x}x-e^{-x}x^2 is e^{-x}x^2-4e^{-x}x+2e^{-x}

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

The first derivative of 2e^{-x}x-e^{-x}x^2 is e^{-x}x^2-4e^{-x}x+2e^{-x}

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

e^{- x} x^{2} - 4 e^{- x} x + 2 e^{- x}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

2 (- e^{- x} x + e^{- x}) - (- e^{- x} x^{2} + 2 e^{- x} x) : e^{- x} x^{2} - 4 e^{- x} x + 2 e^{- x}

= e^{- x} x^{2} - 4 e^{- x} x + 2 e^{- x}

What is the derivative of 2e^{-x}x-e^{-x}x^2 ?
The derivative of 2e^{-x}x-e^{-x}x^2 is e^{-x}x^2-4e^{-x}x+2e^{-x}
What is the first derivative of 2e^{-x}x-e^{-x}x^2 ?
The first derivative of 2e^{-x}x-e^{-x}x^2 is e^{-x}x^2-4e^{-x}x+2e^{-x}