What is the derivative of e^xcos(3x-3e^xsin(3x)) ?

The derivative of e^xcos(3x-3e^xsin(3x)) is -8e^xcos(3x)-6e^xsin(3x)

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

The first derivative of e^xcos(3x-3e^xsin(3x)) is -8e^xcos(3x)-6e^xsin(3x)

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

- 8 e^{x} cos (3 x) - 6 e^{x} sin (3 x)

Solution steps

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

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{x} cos (3 x)) - \frac{d}{d x} (3 e^{x} sin (3 x))

\frac{d}{d x} (e^{x} cos (3 x)) = e^{x} cos (3 x) - 3 e^{x} sin (3 x)

\frac{d}{d x} (3 e^{x} sin (3 x)) = 3 (e^{x} sin (3 x) + cos (3 x) \cdot 3 e^{x})

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

Simplify

e^{x} cos (3 x) - 3 e^{x} sin (3 x) - 3 (e^{x} sin (3 x) + cos (3 x) \cdot 3 e^{x}) : - 8 e^{x} cos (3 x) - 6 e^{x} sin (3 x)

= - 8 e^{x} cos (3 x) - 6 e^{x} sin (3 x)

\int_{0}^{5} π (x^{2}) d x

\int \frac{1}{4 x ^{2} + 10 x + 5} d x

\frac{1}{y} \frac{d y}{d x} = \frac{2}{x}

\int u^{9} d u

\int \frac{1}{8 - 2 x - x ^{2}} d x

What is the derivative of e^xcos(3x-3e^xsin(3x)) ?
The derivative of e^xcos(3x-3e^xsin(3x)) is -8e^xcos(3x)-6e^xsin(3x)
What is the first derivative of e^xcos(3x-3e^xsin(3x)) ?
The first derivative of e^xcos(3x-3e^xsin(3x)) is -8e^xcos(3x)-6e^xsin(3x)