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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} ((sech (2 x))^{s i n (3 x)})

\frac{d}{d x} (x \cdot (x - 1))

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

x \to 7 lim (\frac{1}{x - 7})

\int_{- \infty}^{- 1} x^{- \frac{14}{5}} d x