derivative of arctan(5/x)

Lösung

\frac{d}{d x} (arctan (\frac{5}{x}))

- \frac{5}{25 + x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (arctan (\frac{5}{x}))

Wende die Kettenregel an:

\frac{1}{( \frac{5}{x} ) ^{2} + 1} \frac{d}{d x} (\frac{5}{x})

= \frac{1}{( \frac{5}{x} ) ^{2} + 1} \frac{d}{d x} (\frac{5}{x})

\frac{d}{d x} (\frac{5}{x}) = - \frac{5}{x ^{2}}

= \frac{1}{( \frac{5}{x} ) ^{2} + 1} (- \frac{5}{x ^{2}})

Vereinfache

\frac{1}{( \frac{5}{x} ) ^{2} + 1} (- \frac{5}{x ^{2}}) : - \frac{5}{25 + x ^{2}}

= - \frac{5}{25 + x ^{2}}

d er i v a t i v e \frac{x ^{2} + 2 x - 2}{( x + 1 ) ^{2}}

\frac{\partial}{\partial z} (x z e^{yz})

y^{^{'}} = 0.23 y - 0.0005 y^{2}

\int_{0}^{60} (60 - y)^{2} d y

x y^{^{'}} + y = 3 x y