What is the derivative of sin(2xcos(2x)) ?

The derivative of sin(2xcos(2x)) is 2cos(4x)

What is the first derivative of sin(2xcos(2x)) ?

The first derivative of sin(2xcos(2x)) is 2cos(4x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (sin (2 x) cos (2 x))

2 cos (4 x)

Solution steps

\frac{d}{d x} (sin (2 x) cos (2 x))

Apply the Product Rule:

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

f = sin (2 x), g = cos (2 x)

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

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

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

= cos (2 x) \cdot 2 cos (2 x) + (- sin (2 x) \cdot 2) sin (2 x)

Simplify

cos (2 x) \cdot 2 cos (2 x) + (- sin (2 x) \cdot 2) sin (2 x) : 2 cos (4 x)

= 2 cos (4 x)

f (x) = x^{3}, at x = 6

\int - 9 x d x

x \to 2 lim (51 - x - 7)

f (x) = x - 1, 1, 2

sin (5 t - 10)

What is the derivative of sin(2xcos(2x)) ?
The derivative of sin(2xcos(2x)) is 2cos(4x)
What is the first derivative of sin(2xcos(2x)) ?
The first derivative of sin(2xcos(2x)) is 2cos(4x)