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

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

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simplify e^{(-x^2(ln(2)))}(-2)x(ln(2))

simplify

e^{(- x^{2} (l n (2)))} \cdot (- 2) x \cdot (ln (2))

- ln (2) \cdot 2^{- x^{2} + 1} x

Solution steps

e^{(- x^{2} (l n (2)))} (- 2) x (ln (2))

Apply exponent rule:

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

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

Remove parentheses:

(- a) = - a

= - \frac{1}{e ^{x^{2} l n (2)}} \cdot 2 x ln (2)

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

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 2 = 2

= - \frac{2 ln ( 2 ) x}{2 ^{x^{2}}}

Apply exponent rule:

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

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

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

3 e^{- 0.01 (10)}

17 e^{- \frac{1}{5}}

4 π (1 0^{- 7})

\frac{1}{2} \cdot 165.88 \cdot 1 0^{- 6} \cdot 111. 1^{2}

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