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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

\int sin^{3} (cos^{2} (d) x) d x

\int (14 x^{6} y^{- 4} - 12 x^{5} y^{- 3}) d x

d er i v a t i v e e^{a r c t a n (3 x^{2})}

\frac{d ^{3}}{d x ^{3}} (\frac{x}{x + 1})

\frac{\partial ^{2}}{\partial y ^{2}} (y^{5} sin (3 x))