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

The derivative of (ln(cos^2(x))^2) is -4ln(cos^2(x))tan(x)

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

The first derivative of (ln(cos^2(x))^2) is -4ln(cos^2(x))tan(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

- 4 ln (cos^{2} (x)) tan (x)

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (ln (cos^{2} (x))) = - 2 tan (x)

= 2 ln (cos^{2} (x)) (- 2 tan (x))

Simplify

= - 4 ln (cos^{2} (x)) tan (x)

What is the derivative of (ln(cos^2(x))^2) ?
The derivative of (ln(cos^2(x))^2) is -4ln(cos^2(x))tan(x)
What is the first derivative of (ln(cos^2(x))^2) ?
The first derivative of (ln(cos^2(x))^2) is -4ln(cos^2(x))tan(x)