derivative y=(sin(x))/(1+sin(x))

Lösung

ableitung von

y = \frac{sin ( x )}{1 + sin ( x )}

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

Schritte zur Lösung

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

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

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

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

Multipliziere aus

cos (x) (1 + sin (x)) - cos (x) sin (x) : cos (x)

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

\int \frac{x}{x ^{2} + 3} d x

\int \frac{x ^{3}}{x ^{2} - 49} d x

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

x \to 2 lim (x^{4} + 5^{x} - 2)

x \to - 1 lim (2 x^{3} + 3 x^{2} - 6)