What is (-3e^{3x})(xe^{-x}) ?

The solution to (-3e^{3x})(xe^{-x}) is -3e^{2x}x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (-3e^{3x})(xe^{-x})

simplify

(- 3 e^{3 x}) (x e^{- x})

- 3 e^{2 x} x

Solution steps

(- 3 e^{3 x}) (x e^{- x})

Apply exponent rule:

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

= \frac{1}{e ^{x}} x (- 3 e^{3 x})

Remove parentheses:

(- a) = - a

= - 3 e^{3 x} x \frac{1}{e ^{x}}

Multiply fractions:

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

= - \frac{1 \cdot 3 e ^{3 x} x}{e ^{x}}

Multiply the numbers:

1 \cdot 3 = 3

= - \frac{3 e ^{3 x} x}{e ^{x}}

Apply exponent rule:

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

\frac{e ^{3 x}}{e ^{x}} = e^{3 x - x} = e^{2 x}

= - 3 e^{2 x} x

6.39 \cdot 1 0^{- 5}

(c e^{x}) (c e^{x})

e^{- 0.3 x} (cos (x) + sin (x))

e^{- 5 t} sinh (6 t)

(2.7 \cdot 1 0^{- 6}) \cdot 1 0^{9}