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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d y}{d x} = e^{4 x + 2 y}

\int ((x^{2} + 7)^{2021}) x d x

\int_{1}^{2} \frac{x ^{2} + 1}{3 x - x ^{2}} d x

\frac{d}{d x} ((x + (x + sin^{2} (x))^{3})^{4})

x \to - 4 lim (\frac{x ^{2}}{4 x + 16})