en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify e^{-1/2 x}(xe^{x/2})

Solution

simplify

e^{- \frac{1}{2} x} (x e^{\frac{x}{2}})

Solution

x

Solution steps

e^{- \frac{1}{2} x} (x e^{\frac{x}{2}})

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= e^{\frac{x}{2}} \frac{1}{e ^{\frac{1}{2} x}} x

\frac{1}{e ^{\frac{1}{2} x}} = \frac{1}{e ^{\frac{x}{2}}}

= e^{\frac{x}{2}} \frac{1}{e ^{\frac{x}{2}}} x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot x e ^{\frac{x}{2}}}{e ^{\frac{x}{2}}}

Cancel the common factor:

e^{\frac{x}{2}}

= 1 \cdot x

Multiply:

1 \cdot x = x

= x

Popular Examples

simplify 3e^x*e^x simplify

3 e^{x} \cdot e^{x}

simplify e^{-3t}dt simplify

e^{- 3 t} d t

simplify 150000(1+((0.15)/(12)))^{-(12(6))}simplify

150000 (1 + (\frac{0.15}{12}))^{- (12 (6))}

simplify e^{-ln(cos(x)+1)}simplify

e^{- l n (c o s (x) + 1)}

simplify-(-1)e^{-((-1)^2)/2}simplify

- (- 1) e^{- \frac{( - 1 ) ^{2}}{2}}

Frequently Asked Questions (FAQ)

What is e^{-1/2 x}(xe^{x/2}) ?
The solution to e^{-1/2 x}(xe^{x/2}) is x