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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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