What is the derivative of cos^2(5pix) ?

The derivative of cos^2(5pix) is -10picos(5pix)sin(5pix)

What is the first derivative of cos^2(5pix) ?

The first derivative of cos^2(5pix) is -10picos(5pix)sin(5pix)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

cos^{2} (5 π x)

- 10 π cos (5 π x) sin (5 π x)

Solution steps

\frac{d}{d x} (cos^{2} (5 π x))

Apply the chain rule:

2 cos (5 π x) \frac{d}{d x} (cos (5 π x))

= 2 cos (5 π x) \frac{d}{d x} (cos (5 π x))

\frac{d}{d x} (cos (5 π x)) = - sin (5 π x) \cdot 5 π

= 2 cos (5 π x) (- sin (5 π x) \cdot 5 π)

Simplify

= - 10 π cos (5 π x) sin (5 π x)

What is the derivative of cos^2(5pix) ?
The derivative of cos^2(5pix) is -10picos(5pix)sin(5pix)
What is the first derivative of cos^2(5pix) ?
The first derivative of cos^2(5pix) is -10picos(5pix)sin(5pix)