What is the derivative of ((1-cos(x)))/((1+cos(x))) ?

The derivative of ((1-cos(x)))/((1+cos(x))) is (2sin(x))/((1+cos(x))^2)

What is the first derivative of ((1-cos(x)))/((1+cos(x))) ?

The first derivative of ((1-cos(x)))/((1+cos(x))) is (2sin(x))/((1+cos(x))^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{( 1 - cos ( x ) )}{( 1 + cos ( x ) )}

\frac{2 sin ( x )}{( 1 + cos ( x ) ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 1 - cos ( x ) ) ( 1 + cos ( x ) ) - \frac{d}{d x} ( 1 + cos ( x ) ) ( 1 - cos ( x ) )}{( 1 + cos ( x ) ) ^{2}}

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

\frac{d}{d x} (1 + cos (x)) = - sin (x)

= \frac{sin ( x ) ( 1 + cos ( x ) ) - ( - sin ( x ) ) ( 1 - cos ( x ) )}{( 1 + cos ( x ) ) ^{2}}

Simplify

\frac{sin ( x ) ( 1 + cos ( x ) ) - ( - sin ( x ) ) ( 1 - cos ( x ) )}{( 1 + cos ( x ) ) ^{2}} : \frac{2 sin ( x )}{( 1 + cos ( x ) ) ^{2}}

= \frac{2 sin ( x )}{( 1 + cos ( x ) ) ^{2}}

What is the derivative of ((1-cos(x)))/((1+cos(x))) ?
The derivative of ((1-cos(x)))/((1+cos(x))) is (2sin(x))/((1+cos(x))^2)
What is the first derivative of ((1-cos(x)))/((1+cos(x))) ?
The first derivative of ((1-cos(x)))/((1+cos(x))) is (2sin(x))/((1+cos(x))^2)