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Beliebt Rechnen >

derivative of arctan(c/x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

derivative of 16e^{-2x}

\frac{d}{d x} (16 e^{- 2 x})

integral from 0 to 8 of f(x)

\int_{0}^{8} f (x) d x

(d^2)/(dx^2)(x^{1/2})

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

(\partial)/(\partial s)(arctan(rs))

\frac{\partial}{\partial s} (arctan (rs))

derivative e^{x^x}

d er i v a t i v e e^{x^{x}}