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

The derivative of (ln(cos(2x))/x) is (-2xtan(2x)-ln(cos(2x)))/(x^2)

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

The first derivative of (ln(cos(2x))/x) is (-2xtan(2x)-ln(cos(2x)))/(x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

= \frac{( - 2 tan ( 2 x ) ) x - 1 \cdot ln ( cos ( 2 x ) )}{x ^{2}}

Simplify

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

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