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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int e^{e x} d x

\int (x^{2} + 1 + \frac{1}{x ^{2} + 1}) d x

\int \frac{5}{x ^{3}} d x

\int \frac{cos ( 3 x ) + 3}{sin ( 3 x )} d x

\frac{3}{s ( s + 3 ) + 6}

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