What is (\partial)/(\partial x)(e^{-2x}sin(2x)) ?

The answer to (\partial)/(\partial x)(e^{-2x}sin(2x)) is -2e^{-2x}sin(2x)+2e^{-2x}cos(2x)

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(\partial)/(\partial x)(e^{-2x}sin(2x))

\frac{\partial}{\partial x} (e^{- 2 x} sin (2 x))

- 2 e^{- 2 x} sin (2 x) + 2 e^{- 2 x} cos (2 x)

Solution steps

\frac{\partial}{\partial x} (e^{- 2 x} sin (2 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- 2 x}, g = sin (2 x)

= \frac{\partial}{\partial x} (e^{- 2 x}) sin (2 x) + \frac{\partial}{\partial x} (sin (2 x)) e^{- 2 x}

\frac{\partial}{\partial x} (e^{- 2 x}) = - 2 e^{- 2 x}

\frac{\partial}{\partial x} (sin (2 x)) = cos (2 x) \cdot 2

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

Simplify

= - 2 e^{- 2 x} sin (2 x) + 2 e^{- 2 x} cos (2 x)

\frac{( - 2 s + 24 )}{( s ^{2} - 13 )}

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\frac{d}{d x} (6 x^{3})

What is (\partial)/(\partial x)(e^{-2x}sin(2x)) ?
The answer to (\partial)/(\partial x)(e^{-2x}sin(2x)) is -2e^{-2x}sin(2x)+2e^{-2x}cos(2x)