derivative of (sin(x)/(1-2cos(x)))

Lösung

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

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

Schritte zur Lösung

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

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

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

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

2 sin (x) sin (x) = 2 sin^{2} (x)

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

im pl i c i t \frac{d y}{d x}, y = 7 x^{2} + 6 y x

\int e^{- θ} cos (8 θ) d θ

\frac{\partial}{\partial x} (\frac{1}{x y ^{2} - x ^{2} y})

x \to 0 lim ((e^{x} + x)^{\frac{1}{x}})

(x + 1) \frac{d y}{d x} + y = x ln^{2} (x)