What is e^{2x}*2xe^{-2x} ?

The solution to e^{2x}*2xe^{-2x} is 2x

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simplify e^{2x}*2xe^{-2x}

simplify

e^{2 x} \cdot 2 x e^{- 2 x}

2 x

Solution steps

e^{2 x} \cdot 2 x e^{- 2 x}

Apply exponent rule:

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

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

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

Add similar elements:

2 x - 2 x = 0

= 2 x e^{0}

Apply rule

a^{0} = 1, a \neq = 0

e^{0} = 1

= 2 \cdot 1 \cdot x

Multiply the numbers:

2 \cdot 1 = 2

= 2 x

4 π \cdot 1 0^{- 7} 0.7

(4.9 x 1 0^{- 5}) (3.59 x 1 0^{5})

0.026 \cdot 1 0^{- 8}

1 \cdot 1 0^{- 9.8}

e^{- 3 x} \cdot sin (2 x)