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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

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

\frac{d}{d θ} (sin (θ))

x \to - 5 lim (\frac{( x - 5 )}{x + 5})

l a pl a ce t r an s f or m 8 t^{4}

\int \frac{( x + 4 )}{x ^{2} + 8 x + 17} d x