What is the derivative of e^{-x}(cos(2x+sin(2x))) ?

The derivative of e^{-x}(cos(2x+sin(2x))) is e^{-x}cos(2x)-3e^{-x}sin(2x)

What is the first derivative of e^{-x}(cos(2x+sin(2x))) ?

The first derivative of e^{-x}(cos(2x+sin(2x))) is e^{-x}cos(2x)-3e^{-x}sin(2x)

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

e^{- x} cos (2 x) - 3 e^{- x} sin (2 x)

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (e^{- x}) = - e^{- x}

\frac{d}{d x} (cos (2 x) + sin (2 x)) = - sin (2 x) \cdot 2 + cos (2 x) \cdot 2

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

Simplify

(- e^{- x}) (cos (2 x) + sin (2 x)) + (- sin (2 x) \cdot 2 + cos (2 x) \cdot 2) e^{- x} : e^{- x} cos (2 x) - 3 e^{- x} sin (2 x)

= e^{- x} cos (2 x) - 3 e^{- x} sin (2 x)

e^{- 2 t} cos (3 t) + 5 e^{- 2 t} sin (3 t)

x \to 2 - lim (\frac{x - 2}{x ^{2} - 4})

\frac{x ^{2} - 2}{x ^{2} + 2}

f (x) = 5 3 x

\int sin (6 x) cos (8 x) d x

What is the derivative of e^{-x}(cos(2x+sin(2x))) ?
The derivative of e^{-x}(cos(2x+sin(2x))) is e^{-x}cos(2x)-3e^{-x}sin(2x)
What is the first derivative of e^{-x}(cos(2x+sin(2x))) ?
The first derivative of e^{-x}(cos(2x+sin(2x))) is e^{-x}cos(2x)-3e^{-x}sin(2x)