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

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

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

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

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

Solution steps

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

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

Simplify

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

\frac{d}{d x} (\frac{x + 2}{x + 1})

\int x^{2} e^{x^{2}} d x

\frac{\partial}{\partial y} (e^{x y} y)

\int (3 + x^{8})^{4} 8 x^{7} d x

f (x) = x^{2} - \frac{1}{x}, at x = - 1

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