What is the derivative of 3ln(cos(x)) ?

The derivative of 3ln(cos(x)) is -3tan(x)

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

The first derivative of 3ln(cos(x)) is -3tan(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (3 ln (cos (x)))

- 3 tan (x)

Solution steps

\frac{d}{d x} (3 ln (cos (x)))

Take the constant out:

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

= 3 \frac{d}{d x} (ln (cos (x)))

Apply the chain rule:

\frac{1}{cos ( x )} \frac{d}{d x} (cos (x))

= \frac{1}{cos ( x )} \frac{d}{d x} (cos (x))

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

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

Simplify

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

= - 3 tan (x)

What is the derivative of 3ln(cos(x)) ?
The derivative of 3ln(cos(x)) is -3tan(x)
What is the first derivative of 3ln(cos(x)) ?
The first derivative of 3ln(cos(x)) is -3tan(x)