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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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