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

The solution to e^{-x}(-x+1)(1/2 x^2-2x+1) is ((-x+1)(x^2-4x+2))/(2e^x)

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

simplify

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

\frac{( - x + 1 ) ( x ^{2} - 4 x + 2 )}{2 e ^{x}}

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

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

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

Multiply fractions:

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

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

Multiply:

1 \cdot (- x + 1) = (- x + 1)

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

Join

\frac{x ^{2}}{2} - 2 x + 1 : \frac{x ^{2} - 4 x + 2}{2}

= \frac{\frac{x ^{2} - 4 x + 2}{2} ( - x + 1 )}{e ^{x}}

Multiply

(- x + 1) \frac{x ^{2} - 4 x + 2}{2} : \frac{( x ^{2} - 4 x + 2 ) ( - x + 1 )}{2}

= \frac{\frac{( x ^{2} - 4 x + 2 ) ( - x + 1 )}{2}}{e ^{x}}

Apply the fraction rule:

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

= \frac{( x ^{2} - 4 x + 2 ) ( - x + 1 )}{2 e ^{x}}

(5 + 3) (5 + 3)

f (x) = (e^{- \frac{x}{4}})^{2}

\frac{3937.2 1 ^{2}}{6372. 4 ^{2}}

e^{- (0.05 + 0.005 1 + \frac{7}{12}) \cdot \frac{7}{12}}

What is e^{-x}(-x+1)(1/2 x^2-2x+1) ?
The solution to e^{-x}(-x+1)(1/2 x^2-2x+1) is ((-x+1)(x^2-4x+2))/(2e^x)