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

The derivative of cos^4(3x^2) is -24xcos^3(3x^2)sin(3x^2)

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

The first derivative of cos^4(3x^2) is -24xcos^3(3x^2)sin(3x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

- 24 x cos^{3} (3 x^{2}) sin (3 x^{2})

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

= - 24 x cos^{3} (3 x^{2}) sin (3 x^{2})

What is the derivative of cos^4(3x^2) ?
The derivative of cos^4(3x^2) is -24xcos^3(3x^2)sin(3x^2)
What is the first derivative of cos^4(3x^2) ?
The first derivative of cos^4(3x^2) is -24xcos^3(3x^2)sin(3x^2)