What is e^{t^2}*2te^{-t^2} ?

The solution to e^{t^2}*2te^{-t^2} is 2t

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simplify e^{t^2}*2te^{-t^2}

simplify

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

2 t

Solution steps

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

Apply exponent rule:

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

e^{t^{2}} e^{- t^{2}} = e^{t^{2} - t^{2}}

= 2 t e^{t^{2} - t^{2}}

Add similar elements:

t^{2} - t^{2} = 0

= 2 t e^{0}

Apply rule

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

e^{0} = 1

= 2 \cdot 1 \cdot t

Multiply the numbers:

2 \cdot 1 = 2

= 2 t

e^{- x^{0}}

\frac{d}{d x} (3 (x^{2} + y^{2})^{2})

d esco m p o n er (1 + x^{2})

17.65 e^{- \frac{x}{0.875}}

x - 1 \cdot 2