What is e^{-2t}(2e^{2t}t-e^{2t}+C) ?

The solution to e^{-2t}(2e^{2t}t-e^{2t}+C) is (2e^{2t}t-e^{2t}+C)/(e^{2t)}

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simplify e^{-2t}(2e^{2t}t-e^{2t}+C)

simplify

e^{- 2 t} (2 e^{2 t} t - e^{2 t} + C)

\frac{2 e ^{2 t} t - e ^{2 t} + C}{e ^{2 t}}

Solution steps

e^{- 2 t} (2 e^{2 t} t - e^{2 t} + C)

Apply exponent rule:

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

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

Multiply fractions:

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

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

1 \cdot (2 e^{2 t} t - e^{2 t} + C) = 2 e^{2 t} t - e^{2 t} + C

= \frac{2 e ^{2 t} t - e ^{2 t} + C}{e ^{2 t}}

a^{2} x b^{2}

e^{- \frac{t}{2}}

1.1 \times 1 0^{- 3}

34^{2}

(3 x) (2 x^{2})

What is e^{-2t}(2e^{2t}t-e^{2t}+C) ?
The solution to e^{-2t}(2e^{2t}t-e^{2t}+C) is (2e^{2t}t-e^{2t}+C)/(e^{2t)}