What is 1/32 e^{-2x}(sin(2x)+e^{4x}cos(2x)) ?

The solution to 1/32 e^{-2x}(sin(2x)+e^{4x}cos(2x)) is (sin(2x)+e^{4x}cos(2x))/(32e^{2x)}

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simplify 1/32 e^{-2x}(sin(2x)+e^{4x}cos(2x))

simplify

\frac{1}{32} e^{- 2 x} (sin (2 x) + e^{4 x} cos (2 x))

\frac{sin ( 2 x ) + e ^{4 x} cos ( 2 x )}{32 e ^{2 x}}

Solution steps

\frac{1}{32} e^{- 2 x} (sin (2 x) + e^{4 x} cos (2 x))

Apply exponent rule:

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

= \frac{1}{32} \cdot \frac{1}{e ^{2 x}} (sin (2 x) + e^{4 x} cos (2 x))

Multiply fractions:

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

= \frac{1 \cdot 1 \cdot ( sin ( 2 x ) + e ^{4 x} cos ( 2 x ) )}{32 e ^{2 x}}

1 \cdot 1 \cdot (sin (2 x) + e^{4 x} cos (2 x)) = sin (2 x) + e^{4 x} cos (2 x)

= \frac{sin ( 2 x ) + e ^{4 x} cos ( 2 x )}{32 e ^{2 x}}

e^{2} e^{- 1}

e^{2} e^{- 2}

\frac{1}{2} \cdot e^{- 2 \cdot \frac{1}{2}}

What is 1/32 e^{-2x}(sin(2x)+e^{4x}cos(2x)) ?
The solution to 1/32 e^{-2x}(sin(2x)+e^{4x}cos(2x)) is (sin(2x)+e^{4x}cos(2x))/(32e^{2x)}