What is the derivative of 3(5e^{5x}cos(6x)-6e^{5x}sin(6x)) ?

The derivative of 3(5e^{5x}cos(6x)-6e^{5x}sin(6x)) is 3(-11e^{5x}cos(6x)-60e^{5x}sin(6x))

What is the first derivative of 3(5e^{5x}cos(6x)-6e^{5x}sin(6x)) ?

The first derivative of 3(5e^{5x}cos(6x)-6e^{5x}sin(6x)) is 3(-11e^{5x}cos(6x)-60e^{5x}sin(6x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

3 (5 e^{5 x} cos (6 x) - 6 e^{5 x} sin (6 x))

3 (- 11 e^{5 x} cos (6 x) - 60 e^{5 x} sin (6 x))

Solution steps

\frac{d}{d x} (3 (5 e^{5 x} cos (6 x) - 6 e^{5 x} sin (6 x)))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (5 e^{5 x} cos (6 x) - 6 e^{5 x} sin (6 x))

Apply the Sum/Difference Rule:

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

= 3 (\frac{d}{d x} (5 e^{5 x} cos (6 x)) - \frac{d}{d x} (6 e^{5 x} sin (6 x)))

\frac{d}{d x} (5 e^{5 x} cos (6 x)) = 5 (5 e^{5 x} cos (6 x) - 6 e^{5 x} sin (6 x))

\frac{d}{d x} (6 e^{5 x} sin (6 x)) = 6 (e^{5 x} \cdot 5 sin (6 x) + cos (6 x) \cdot 6 e^{5 x})

= 3 (5 (5 e^{5 x} cos (6 x) - 6 e^{5 x} sin (6 x)) - 6 (e^{5 x} \cdot 5 sin (6 x) + cos (6 x) \cdot 6 e^{5 x}))

Expand

5 (5 e^{5 x} cos (6 x) - 6 e^{5 x} sin (6 x)) - 6 (e^{5 x} \cdot 5 sin (6 x) + cos (6 x) \cdot 6 e^{5 x}) : - 11 e^{5 x} cos (6 x) - 60 e^{5 x} sin (6 x)

= 3 (- 11 e^{5 x} cos (6 x) - 60 e^{5 x} sin (6 x))

What is the derivative of 3(5e^{5x}cos(6x)-6e^{5x}sin(6x)) ?
The derivative of 3(5e^{5x}cos(6x)-6e^{5x}sin(6x)) is 3(-11e^{5x}cos(6x)-60e^{5x}sin(6x))
What is the first derivative of 3(5e^{5x}cos(6x)-6e^{5x}sin(6x)) ?
The first derivative of 3(5e^{5x}cos(6x)-6e^{5x}sin(6x)) is 3(-11e^{5x}cos(6x)-60e^{5x}sin(6x))