What is the derivative of y=cos^4(x)-sin^4(x) ?

The derivative of y=cos^4(x)-sin^4(x) is -sin(2x)*2

What is the first derivative of y=cos^4(x)-sin^4(x) ?

The first derivative of y=cos^4(x)-sin^4(x) is -sin(2x)*2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

y = cos^{4} (x) - sin^{4} (x)

- sin (2 x) \cdot 2

Solution steps

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

Simplify

cos^{4} (x) - sin^{4} (x) : cos (2 x)

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

Apply the chain rule:

- sin (2 x) \frac{d}{d x} (2 x)

= - sin (2 x) \frac{d}{d x} (2 x)

\frac{d}{d x} (2 x) = 2

= - sin (2 x) \cdot 2

What is the derivative of y=cos^4(x)-sin^4(x) ?
The derivative of y=cos^4(x)-sin^4(x) is -sin(2x)*2
What is the first derivative of y=cos^4(x)-sin^4(x) ?
The first derivative of y=cos^4(x)-sin^4(x) is -sin(2x)*2