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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

x \to 0 + lim (x ln (3 x))

d er i v a t i v e \frac{6 x}{5 - cot ( x )}

d er i v a t i v e e^{2 x^{2 x}}

x \to 1 lim ((x - 1)^{- 1})

t an g e n t f (x) = cos^{3} (x), at (0)