What is ye^{-y}(y-2/3) ?

The solution to ye^{-y}(y-2/3) is (y(3y-2))/(3e^y)

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simplify ye^{-y}(y-2/3)

simplify

y e^{- y} (y - \frac{2}{3})

\frac{y ( 3 y - 2 )}{3 e ^{y}}

Solution steps

y e^{- y} (y - \frac{2}{3})

Apply exponent rule:

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

= \frac{1}{e ^{y}} y (y - \frac{2}{3})

Multiply fractions:

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

= \frac{1 \cdot y ( y - \frac{2}{3} )}{e ^{y}}

Multiply:

1 \cdot y = y

= \frac{y ( y - \frac{2}{3} )}{e ^{y}}

Join

y - \frac{2}{3} : \frac{3 y - 2}{3}

= \frac{y \frac{3 y - 2}{3}}{e ^{y}}

Multiply

y \frac{y \cdot 3 - 2}{3} : \frac{y ( 3 y - 2 )}{3}

= \frac{\frac{y ( 3 y - 2 )}{3}}{e ^{y}}

Apply the fraction rule:

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

= \frac{( y \cdot 3 - 2 ) y}{3 e ^{y}}

2.57 \cdot 1 0^{- 8} \cdot 2

4.82 \cdot 1 0^{- 4}

e^{x^{2}} e^{x^{- 2}}

4.82 \cdot 1 0^{- 5}

e^{- (a t)^{b}}