derivative y=(1-cos(x))/(sin(x))

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= - (- csc^{2} (x)) - cot (x) csc (x)

Vereinfache

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

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

\frac{\partial}{\partial y} (6 x e^{x^{2} + y^{2}})

\frac{\partial}{\partial y} (x^{2} e^{x^{2} y})

t an g e n t ln (x^{2} - 8 x + 1) (8)

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

\int (\frac{cot ^{2} ( x )}{cos ^{2} ( x )}) d x