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

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

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

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

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{cos ( x )}{sin ( x ) + cos ( x )})

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

f (x) = \frac{e ^{x}}{x ^{2} + 4}, x = 1

f (x) = \frac{x + 1}{x - 2}

\int 0 d x

x^{4} - 3 x^{3} + 2 x^{2} - x + 1

f (x) = x^{5} cos (2 x)

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