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

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

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

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

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

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

Solution steps

\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}}

= \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)

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

Simplify

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

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

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

\int 30 sin^{3} (x co) s^{2} x d x

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

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