What is the derivative of 9cos^3(x) ?

The derivative of 9cos^3(x) is -27cos^2(x)sin(x)

What is the first derivative of 9cos^3(x) ?

The first derivative of 9cos^3(x) is -27cos^2(x)sin(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

9 cos^{3} (x)

- 27 cos^{2} (x) sin (x)

Solution steps

\frac{d}{d x} (9 cos^{3} (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 9 \frac{d}{d x} (cos^{3} (x))

Apply the chain rule:

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

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

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

= 9 \cdot 3 (cos (x))^{2} (- sin (x))

Simplify

= - 27 cos^{2} (x) sin (x)

What is the derivative of 9cos^3(x) ?
The derivative of 9cos^3(x) is -27cos^2(x)sin(x)
What is the first derivative of 9cos^3(x) ?
The first derivative of 9cos^3(x) is -27cos^2(x)sin(x)