derivative arctan(2/x)

Lösung

ableitung von

arctan (\frac{2}{x})

- \frac{2}{4 + x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (arctan (\frac{2}{x}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{( \frac{2}{x} ) ^{2} + 1} (- \frac{2}{x ^{2}}) : - \frac{2}{4 + x ^{2}}

= - \frac{2}{4 + x ^{2}}

x^{2} y^{^{''}} + y^{^{'}} = 0

\int_{0}^{1} x^{6} (1 + 2 x^{7})^{5} d x

d er i v a t i v e f (x) = x^{4} sec (5 x)

\int_{2}^{\infty} e^{- 5 x} d x

\frac{d}{d x} (2 x^{2} + cos^{2} (x))