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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

n = 0 \sum \infty \frac{4 n}{- 4 n + 7}

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

f (x) = 30 + 10 e^{- 0.05 x}

cos^{2} (t)

\frac{\partial}{\partial x} (7 e^{x y} \cdot cos (x yz))

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