What is expand (-2x(x+1)e^2+3e^{2x}-3)/(2e^2) ?

The solution to expand (-2x(x+1)e^2+3e^{2x}-3)/(2e^2) is -x^2-x+(3e^{2x-2})/2-3/(2e^2)

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

expand

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

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

Solution steps

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

Expand

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

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

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

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

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

Cancel

\frac{2 e ^{2} x ^{2}}{2 e ^{2}} : x^{2}

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

Cancel

\frac{2 e ^{2} x}{2 e ^{2}} : x

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

Cancel

\frac{3 e ^{2 x}}{2 e ^{2}} : \frac{3 e ^{2 x - 2}}{2}

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

\frac{\partial}{\partial x} ((z) (sin (z) - x yz))

(e^{3 x} - e^{- 3 x}) (e^{3 x} + e^{- 3 x})

- 3 (5 + 7)

a (1, - 3) b (5, 6)

5 (sin (x) + x cos (x))

What is expand (-2x(x+1)e^2+3e^{2x}-3)/(2e^2) ?
The solution to expand (-2x(x+1)e^2+3e^{2x}-3)/(2e^2) is -x^2-x+(3e^{2x-2})/2-3/(2e^2)