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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

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

= 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

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

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

\frac{x}{x + 17}

y = 9 - x^{2}, y = 4 x

\int \frac{x}{( 1 + x ^{2} ) ^{3}} d x

(2 x + 5)^{2}

\int_{- 1}^{0} x^{\frac{1}{3}} - x^{\frac{2}{3}} d x

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