What is expand (-6e^{-5x}x-(11e^{-5x})/5)xe^{5x} ?

The solution to expand (-6e^{-5x}x-(11e^{-5x})/5)xe^{5x} is -6x^2-(11x)/5

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expand (-6e^{-5x}x-(11e^{-5x})/5)xe^{5x}

expand

(- 6 e^{- 5 x} x - \frac{11 e ^{- 5 x}}{5}) x e^{5 x}

- 6 x^{2} - \frac{11 x}{5}

Solution steps

(- 6 e^{- 5 x} x - \frac{11 e ^{- 5 x}}{5}) x e^{5 x}

= e^{5 x} x (- 6 e^{- 5 x} x - \frac{11 e ^{- 5 x}}{5})

Apply the distributive law:

a (b - c) = ab - a c

a = x e^{5 x}, b = - 6 e^{- 5 x} x, c = \frac{11 e ^{- 5 x}}{5}

= x e^{5 x} (- 6 e^{- 5 x} x) - x e^{5 x} \frac{11 e ^{- 5 x}}{5}

Apply minus-plus rules

+ (- a) = - a

= - 6 e^{5 x} e^{- 5 x} xx - e^{5 x} \frac{11 e ^{- 5 x}}{5} x

Simplify

- 6 e^{5 x} e^{- 5 x} xx - e^{5 x} \frac{11 e ^{- 5 x}}{5} x : - 6 x^{2} - \frac{11 x}{5}

= - 6 x^{2} - \frac{11 x}{5}

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What is expand (-6e^{-5x}x-(11e^{-5x})/5)xe^{5x} ?
The solution to expand (-6e^{-5x}x-(11e^{-5x})/5)xe^{5x} is -6x^2-(11x)/5