What is cos(3x)e^{2t}\times 3e^{2t}cos(3x) ?

The solution to cos(3x)e^{2t}\times 3e^{2t}cos(3x) is 3e^{4t}cos^2(3x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify cos(3x)e^{2t}\times 3e^{2t}cos(3x)

simplify

cos (3 x) e^{2 t} \cdot 3 e^{2 t} cos (3 x)

3 e^{4 t} cos^{2} (3 x)

Solution steps

cos (3 x) e^{2 t} \cdot 3 e^{2 t} cos (3 x)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

cos (3 x) cos (3 x) = cos^{1 + 1} (3 x)

= e^{2 t} \cdot 3 e^{2 t} cos^{1 + 1} (3 x)

Add the numbers:

1 + 1 = 2

= e^{2 t} \cdot 3 e^{2 t} cos^{2} (3 x)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{2 t} e^{2 t} = e^{2 t + 2 t}

= 3 e^{2 t + 2 t} cos^{2} (3 x)

Add similar elements:

2 t + 2 t = 4 t

= 3 e^{4 t} cos^{2} (3 x)

(f \circ f) x + 1

e^{e} \cdot e

(x - 3)^{2} (x - 5)^{2}

e^{- 1.05}

What is cos(3x)e^{2t}\times 3e^{2t}cos(3x) ?
The solution to cos(3x)e^{2t}\times 3e^{2t}cos(3x) is 3e^{4t}cos^2(3x)