What is expand e^x(xe^{-x}-e^{-x}) ?

The solution to expand e^x(xe^{-x}-e^{-x}) is x-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand e^x(xe^{-x}-e^{-x})

expand

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

x - 1

Solution steps

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

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

Apply the distributive law:

a (b - c) = ab - a c

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

= e^{x} x e^{- x} - e^{x} e^{- x}

= e^{x} e^{- x} x - e^{x} e^{- x}

Simplify

e^{x} e^{- x} x - e^{x} e^{- x} : x - 1

= x - 1

x (\frac{( 3 x - 10 ) ^{3}}{100} + 10)

m sin (\frac{π}{6} (k + 1)) + n cos (\frac{π}{6} (k + 1))

(36 + a^{2} + 64 + b^{2})^{2}

(x + 3 - 5) (x + 3 + 5)

\frac{a ^{4 b} x ^{y b}}{c ^{(k - 2) b}}

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