What is the derivative of 4e^{3x}cos(4x) ?

The derivative of 4e^{3x}cos(4x) is 4(3e^{3x}cos(4x)-4e^{3x}sin(4x))

What is the first derivative of 4e^{3x}cos(4x) ?

The first derivative of 4e^{3x}cos(4x) is 4(3e^{3x}cos(4x)-4e^{3x}sin(4x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

4 e^{3 x} cos (4 x)

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

Solution steps

\frac{d}{d x} (4 e^{3 x} cos (4 x))

Take the constant out:

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

= 4 \frac{d}{d x} (e^{3 x} cos (4 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{3 x}, g = cos (4 x)

= 4 (\frac{d}{d x} (e^{3 x}) cos (4 x) + \frac{d}{d x} (cos (4 x)) e^{3 x})

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

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

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

Simplify

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

What is the derivative of 4e^{3x}cos(4x) ?
The derivative of 4e^{3x}cos(4x) is 4(3e^{3x}cos(4x)-4e^{3x}sin(4x))
What is the first derivative of 4e^{3x}cos(4x) ?
The first derivative of 4e^{3x}cos(4x) is 4(3e^{3x}cos(4x)-4e^{3x}sin(4x))