What is the derivative of (sin(3x)^4) ?

The derivative of (sin(3x)^4) is 12sin^3(3x)cos(3x)

What is the first derivative of (sin(3x)^4) ?

The first derivative of (sin(3x)^4) is 12sin^3(3x)cos(3x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} ((sin (3 x))^{4})

12 sin^{3} (3 x) cos (3 x)

Solution steps

\frac{d}{d x} ((sin (3 x))^{4})

Apply the chain rule:

4 (sin (3 x))^{3} \frac{d}{d x} (sin (3 x))

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

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

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

Simplify

= 12 sin^{3} (3 x) cos (3 x)

What is the derivative of (sin(3x)^4) ?
The derivative of (sin(3x)^4) is 12sin^3(3x)cos(3x)
What is the first derivative of (sin(3x)^4) ?
The first derivative of (sin(3x)^4) is 12sin^3(3x)cos(3x)