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

Lösung

\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}}

Schritte zur Lösung

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

Vereinfache

\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}}

\int \frac{2 x}{1 - 4 x ^{4}} d x

\int \frac{z ^{2}}{z ^{3} + 1} d z

d er i v a t i v e - 9 (5 x^{2} + 4)^{- 6}

\int e^{t a n (x)} sec^{2} (x) d x

\frac{d}{d t} (3^{t})