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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

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

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

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

Simplify

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

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

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