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

The derivative of sin^3(x+sin(3x)) is 3sin^2(x)cos(x)+cos(3x)*3

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

The first derivative of sin^3(x+sin(3x)) is 3sin^2(x)cos(x)+cos(3x)*3

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) + sin (3 x))

3 sin^{2} (x) cos (x) + cos (3 x) \cdot 3

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (sin^{3} (x)) = 3 sin^{2} (x) cos (x)

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

= 3 sin^{2} (x) cos (x) + cos (3 x) \cdot 3

What is the derivative of sin^3(x+sin(3x)) ?
The derivative of sin^3(x+sin(3x)) is 3sin^2(x)cos(x)+cos(3x)*3
What is the first derivative of sin^3(x+sin(3x)) ?
The first derivative of sin^3(x+sin(3x)) is 3sin^2(x)cos(x)+cos(3x)*3