What is the derivative of-1/4 cos^4(x) ?

The derivative of-1/4 cos^4(x) is cos^3(x)sin(x)

What is the first derivative of-1/4 cos^4(x) ?

The first derivative of-1/4 cos^4(x) is cos^3(x)sin(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

- \frac{1}{4} cos^{4} (x)

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

Solution steps

\frac{d}{d x} (- \frac{1}{4} cos^{4} (x))

Take the constant out:

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

= - \frac{1}{4} \frac{d}{d x} (cos^{4} (x))

Apply the chain rule:

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

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

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

= - \frac{1}{4} \cdot 4 (cos (x))^{3} (- sin (x))

Simplify

- \frac{1}{4} \cdot 4 cos^{3} (x) (- sin (x)) : cos^{3} (x) sin (x)

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

What is the derivative of-1/4 cos^4(x) ?
The derivative of-1/4 cos^4(x) is cos^3(x)sin(x)
What is the first derivative of-1/4 cos^4(x) ?
The first derivative of-1/4 cos^4(x) is cos^3(x)sin(x)