What is expand (e^{-x}cos(e^{-x})-sin(e^{-x}))e^{2x} ?

The solution to expand (e^{-x}cos(e^{-x})-sin(e^{-x}))e^{2x} is e^xcos(e^{-x})-e^{2x}sin(e^{-x})

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expand (e^{-x}cos(e^{-x})-sin(e^{-x}))e^{2x}

expand

(e^{- x} cos (e^{- x}) - sin (e^{- x})) e^{2 x}

e^{x} cos (e^{- x}) - e^{2 x} sin (e^{- x})

Solution steps

(e^{- x} cos (e^{- x}) - sin (e^{- x})) e^{2 x}

= e^{2 x} (e^{- x} cos (e^{- x}) - sin (e^{- x}))

Apply the distributive law:

a (b - c) = ab - a c

a = e^{2 x}, b = e^{- x} cos (e^{- x}), c = sin (e^{- x})

= e^{2 x} e^{- x} cos (e^{- x}) - e^{2 x} sin (e^{- x})

e^{2 x} e^{- x} cos (e^{- x}) = e^{x} cos (e^{- x})

= e^{x} cos (e^{- x}) - e^{2 x} sin (e^{- x})

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What is expand (e^{-x}cos(e^{-x})-sin(e^{-x}))e^{2x} ?
The solution to expand (e^{-x}cos(e^{-x})-sin(e^{-x}))e^{2x} is e^xcos(e^{-x})-e^{2x}sin(e^{-x})