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}}

\int \frac{1}{( 25 - y ^{2} ) - x ^{2}} d x

l a pl a ce t r an s f or m sin (2 t) + 2 cos (2 t) + e^{- t} sin (2 t)

y^{^{'}} = 3 y^{2}

n = 1 \sum \infty 8^{n} x^{n} n!

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