What is the derivative of cos^6(3x^2+4) ?

The derivative of cos^6(3x^2+4) is -36xcos^5(3x^2+4)sin(3x^2+4)

What is the first derivative of cos^6(3x^2+4) ?

The first derivative of cos^6(3x^2+4) is -36xcos^5(3x^2+4)sin(3x^2+4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (cos^{6} (3 x^{2} + 4))

- 36 x cos^{5} (3 x^{2} + 4) sin (3 x^{2} + 4)

Solution steps

\frac{d}{d x} (cos^{6} (3 x^{2} + 4))

Apply the chain rule:

6 (cos (3 x^{2} + 4))^{5} \frac{d}{d x} (cos (3 x^{2} + 4))

= 6 (cos (3 x^{2} + 4))^{5} \frac{d}{d x} (cos (3 x^{2} + 4))

\frac{d}{d x} (cos (3 x^{2} + 4)) = - sin (3 x^{2} + 4) \cdot 6 x

= 6 (cos (3 x^{2} + 4))^{5} (- sin (3 x^{2} + 4) \cdot 6 x)

Simplify

= - 36 x cos^{5} (3 x^{2} + 4) sin (3 x^{2} + 4)

What is the derivative of cos^6(3x^2+4) ?
The derivative of cos^6(3x^2+4) is -36xcos^5(3x^2+4)sin(3x^2+4)
What is the first derivative of cos^6(3x^2+4) ?
The first derivative of cos^6(3x^2+4) is -36xcos^5(3x^2+4)sin(3x^2+4)