derivative of arctan(1/(3x))

Lösung

\frac{d}{d x} (arctan (\frac{1}{3 x}))

- \frac{3}{1 + 9 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (arctan (\frac{1}{3 x}))

Wende die Kettenregel an:

\frac{1}{( \frac{1}{3 x} ) ^{2} + 1} \frac{d}{d x} (\frac{1}{3 x})

= \frac{1}{( \frac{1}{3 x} ) ^{2} + 1} \frac{d}{d x} (\frac{1}{3 x})

\frac{d}{d x} (\frac{1}{3 x}) = - \frac{1}{3 x ^{2}}

= \frac{1}{( \frac{1}{3 x} ) ^{2} + 1} (- \frac{1}{3 x ^{2}})

Vereinfache

\frac{1}{( \frac{1}{3 x} ) ^{2} + 1} (- \frac{1}{3 x ^{2}}) : - \frac{3}{1 + 9 x ^{2}}

= - \frac{3}{1 + 9 x ^{2}}

\frac{d}{d r} (\frac{r}{r ^{2} + 5})

t \to 3 lim (\frac{2 t - 3}{t - 3})

s l o p e y = 5 sec (x) - 10 cos (x), (\frac{π}{3}, 5)

d er i v a t i v e y = arcsin (3 5 x)

x \to 1 lim (2 3 x^{2} + 1)