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Popular >

expand (1+e^{-x})e^x

Solution

expand

(1 + e^{- x}) e^{x}

Solution

e^{x} + 1

Solution steps

(1 + e^{- x}) e^{x}

= e^{x} (1 + e^{- x})

Apply the distributive law:

a (b + c) = ab + a c

a = e^{x}, b = 1, c = e^{- x}

= e^{x} \cdot 1 + e^{x} e^{- x}

= 1 \cdot e^{x} + e^{x} e^{- x}

Simplify

1 \cdot e^{x} + e^{x} e^{- x} : e^{x} + 1

= e^{x} + 1

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Frequently Asked Questions (FAQ)

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