What is e(-(x^2)/(e^x)-x/(e^x)-1/(e^x))*e^{x-1} ?

The solution to e(-(x^2)/(e^x)-x/(e^x)-1/(e^x))*e^{x-1} is -x^2-x-1

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simplify e(-(x^2)/(e^x)-x/(e^x)-1/(e^x))*e^{x-1}

simplify

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

- x^{2} - x - 1

Solution steps

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e e^{x - 1} = e^{1 + x - 1}

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

Combine the fractions

- \frac{x ^{2}}{e ^{x}} - \frac{x}{e ^{x}} - \frac{1}{e ^{x}} : \frac{- x ^{2} - x - 1}{e ^{x}}

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

Remove parentheses:

(a) = a

= \frac{- x ^{2} - x - 1}{e ^{x}} e^{1 + x - 1}

Simplify

1 + x - 1 : x

= e^{x} \frac{- x ^{2} - x - 1}{e ^{x}}

Multiply fractions:

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

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

Cancel the common factor:

e^{x}

= - - x^{2} - x - 1

2 e^{- 0.03 \cdot \frac{1.5}{12}}

\frac{( x + 1 )}{( x - 1 )}

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

8.82 x^{0.4} x sin (45. 5^{\circ})

(a^{2} + b^{2})^{2} \cdot (a^{2} - b^{2})^{2}

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