What is the derivative of-11e^xsin(2x-2e^xcos(2x)) ?

The derivative of-11e^xsin(2x-2e^xcos(2x)) is -7e^xsin(2x)-24e^xcos(2x)

What is the first derivative of-11e^xsin(2x-2e^xcos(2x)) ?

The first derivative of-11e^xsin(2x-2e^xcos(2x)) is -7e^xsin(2x)-24e^xcos(2x)

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\frac{d}{d x} (- 11 e^{x} sin (2 x) - 2 e^{x} cos (2 x))

- 7 e^{x} sin (2 x) - 24 e^{x} cos (2 x)

Solution steps

\frac{d}{d x} (- 11 e^{x} sin (2 x) - 2 e^{x} cos (2 x))

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (11 e^{x} sin (2 x)) - \frac{d}{d x} (2 e^{x} cos (2 x))

\frac{d}{d x} (11 e^{x} sin (2 x)) = 11 (e^{x} sin (2 x) + cos (2 x) \cdot 2 e^{x})

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

= - 11 (e^{x} sin (2 x) + cos (2 x) \cdot 2 e^{x}) - 2 (e^{x} cos (2 x) - 2 e^{x} sin (2 x))

Simplify

- 11 (e^{x} sin (2 x) + cos (2 x) \cdot 2 e^{x}) - 2 (e^{x} cos (2 x) - 2 e^{x} sin (2 x)) : - 7 e^{x} sin (2 x) - 24 e^{x} cos (2 x)

= - 7 e^{x} sin (2 x) - 24 e^{x} cos (2 x)

y = x^{2} + 8, (4, 24)

(x^{2} + 1) y^{^{'}} + 9 x (y - 1) = 0

\int \frac{1}{csc ( x ) - 1} d x

x \to 0 lim (\frac{5 e ^{x} - 5}{x})

\int (cos (x))^{4} d x

What is the derivative of-11e^xsin(2x-2e^xcos(2x)) ?
The derivative of-11e^xsin(2x-2e^xcos(2x)) is -7e^xsin(2x)-24e^xcos(2x)
What is the first derivative of-11e^xsin(2x-2e^xcos(2x)) ?
The first derivative of-11e^xsin(2x-2e^xcos(2x)) is -7e^xsin(2x)-24e^xcos(2x)