derivative of arctan(8/x)

Lösung

\frac{d}{d x} (arctan (\frac{8}{x}))

- \frac{8}{64 + x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (arctan (\frac{8}{x}))

Wende die Kettenregel an:

\frac{1}{( \frac{8}{x} ) ^{2} + 1} \frac{d}{d x} (\frac{8}{x})

= \frac{1}{( \frac{8}{x} ) ^{2} + 1} \frac{d}{d x} (\frac{8}{x})

\frac{d}{d x} (\frac{8}{x}) = - \frac{8}{x ^{2}}

= \frac{1}{( \frac{8}{x} ) ^{2} + 1} (- \frac{8}{x ^{2}})

Vereinfache

\frac{1}{( \frac{8}{x} ) ^{2} + 1} (- \frac{8}{x ^{2}}) : - \frac{8}{64 + x ^{2}}

= - \frac{8}{64 + x ^{2}}

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

a re a y = - x^{2} + 16, y = \frac{- x}{4} - 1, 4 (y + 6.5) = 6.5 x

d er i v a t i v e (3 x^{2} - 6 x + 6) e^{- 5 x}

\int_{0}^{2} sin^{2} (x co) s^{2} 2 x

\int \frac{5}{4 + 9 x ^{2}} d x