What is the derivative of e^xcos(2x-2e^xsin(2x)) ?

The derivative of e^xcos(2x-2e^xsin(2x)) is -3e^xcos(2x)-4e^xsin(2x)

What is the first derivative of e^xcos(2x-2e^xsin(2x)) ?

The first derivative of e^xcos(2x-2e^xsin(2x)) is -3e^xcos(2x)-4e^xsin(2x)

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

- 3 e^{x} cos (2 x) - 4 e^{x} sin (2 x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

e^{x} cos (2 x) - 2 e^{x} sin (2 x) - 2 (e^{x} sin (2 x) + cos (2 x) \cdot 2 e^{x}) : - 3 e^{x} cos (2 x) - 4 e^{x} sin (2 x)

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

\frac{\partial}{\partial y} (2 y)

\int \frac{3}{x 4 - x ^{2}} d x

(- 2, 1), (1, 6)

\frac{d}{d x} (e^{(3 - 2 x)})

\frac{d}{d u} (u^{- 1})

What is the derivative of e^xcos(2x-2e^xsin(2x)) ?
The derivative of e^xcos(2x-2e^xsin(2x)) is -3e^xcos(2x)-4e^xsin(2x)
What is the first derivative of e^xcos(2x-2e^xsin(2x)) ?
The first derivative of e^xcos(2x-2e^xsin(2x)) is -3e^xcos(2x)-4e^xsin(2x)