What is (e^{x/2}*cos(2x))*(e^{x/2}*cos(x)) ?

The solution to (e^{x/2}*cos(2x))*(e^{x/2}*cos(x)) is e^xcos(2x)cos(x)

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simplify (e^{x/2}cos(2x))(e^{x/2}*cos(x))

simplify

(e^{\frac{x}{2}} \cdot cos (2 x)) \cdot (e^{\frac{x}{2}} \cdot cos (x))

e^{x} cos (2 x) cos (x)

Solution steps

(e^{\frac{x}{2}} cos (2 x)) (e^{\frac{x}{2}} cos (x))

Apply exponent rule:

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

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

= cos (2 x) e^{\frac{x}{2} + \frac{x}{2}} cos (x)

Combine the fractions

\frac{x}{2} + \frac{x}{2} : x

= e^{x} cos (2 x) cos (x)

e^{- (- 7)^{2}}

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

\frac{( 3 \cdot 1 0 ^{8} )}{1.177 \cdot 1 0 ^{- 7}} \cdot 6.63 \cdot 1 0^{- 34}

(\frac{2 e ^{- 4}}{6})^{- 3}

3.28 \cdot 1 0^{- 12}

What is (e^{x/2}*cos(2x))*(e^{x/2}*cos(x)) ?
The solution to (e^{x/2}*cos(2x))*(e^{x/2}*cos(x)) is e^xcos(2x)cos(x)