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

Lösung

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

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

\frac{\partial}{\partial x} (3 x - 3 y^{2} + z^{2})

\int (x - e^{- x})^{2} d x

t an g e n t f (x) = \frac{x ^{2}}{x - 7}

\frac{d}{d x} (5 x - 6)

\int \frac{x + 15}{x ^{2} + 16 x + 68} d x