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

Lösung

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

\frac{csc ( x ) ( cot ^{2} ( x ) - csc ( x ) )}{1 - csc ( x )}

Schritte zur Lösung

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

\frac{d}{d x} (cot (x)) = - csc^{2} (x)

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

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

Vereinfache

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

= \frac{csc ( x ) ( cot ^{2} ( x ) - csc ( x ) )}{1 - csc ( x )}

\frac{d}{d x} (sin (8 x) e^{4 x})

d er i v a t i v e ln (x^{2} - 4)

\int sin (x) (- 8 x cos (2 x)) d x

x \to 0 lim (3 x + 2)

f (x) = \frac{2}{3 x}