derivative of arccot(x+arccot(1/x))

Lösung

\frac{d}{d x} (arccot (x) + arccot (\frac{1}{x}))

0

Schritte zur Lösung

\frac{d}{d x} (arccot (x) + arccot (\frac{1}{x}))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (arccot (x)) + \frac{d}{d x} (arccot (\frac{1}{x}))

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

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

= - \frac{1}{x ^{2} + 1} + \frac{1}{1 + x ^{2}}

Vereinfache

- \frac{1}{x ^{2} + 1} + \frac{1}{1 + x ^{2}} : 0

= 0

\frac{\partial}{\partial x} (\frac{8}{x})

\frac{d}{d t} (ln ((\frac{a + b t}{a - b t})^{\frac{1}{2}}))

d er i v a t i v e arctan (9 t)

\int_{0}^{2} x^{2} e^{- 9 x} d x

\frac{d}{d x} (6 (sec (x) - tan (x))^{\frac{3}{2}})