derivative of (sin(x)/(2+cos(x)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\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}}

Vereinfache

\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

x \to 1 lim (6 2 - x)

\frac{d}{d x} (9 x^{8})

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

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