What is expand e^x(e^y+2ye^{-x}) ?

The solution to expand e^x(e^y+2ye^{-x}) is e^{y+x}+2y

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expand e^x(e^y+2ye^{-x})

expand

e^{x} (e^{y} + 2 y e^{- x})

e^{y + x} + 2 y

Solution steps

e^{x} (e^{y} + 2 y e^{- x})

= e^{x} (e^{y} + 2 e^{- x} y)

Apply the distributive law:

a (b + c) = ab + a c

a = e^{x}, b = e^{y}, c = 2 y e^{- x}

= e^{x} e^{y} + e^{x} \cdot 2 y e^{- x}

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

Simplify

e^{y} e^{x} + 2 e^{x} e^{- x} y : e^{y + x} + 2 y

= e^{y + x} + 2 y

\frac{d}{d x} ((z) (x + 2 y + z - 2 x y z))

(2 e + 4)^{2}

\frac{( x + 4 ) 3}{4}

(\frac{x}{y} + ln (x) + sin (y)) d y

What is expand e^x(e^y+2ye^{-x}) ?
The solution to expand e^x(e^y+2ye^{-x}) is e^{y+x}+2y