derivative arctan(9/x)+arctan(3/x)

Lösung

ableitung von

arctan (\frac{9}{x}) + arctan (\frac{3}{x})

\frac{- 12 x ^{2} - 324}{( x ^{2} + 9 ) ( x ^{2} + 81 )}

Schritte zur Lösung

\frac{d}{d x} (arctan (\frac{9}{x}) + arctan (\frac{3}{x}))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (arctan (\frac{9}{x})) + \frac{d}{d x} (arctan (\frac{3}{x}))

\frac{d}{d x} (arctan (\frac{9}{x})) = - \frac{9}{81 + x ^{2}}

\frac{d}{d x} (arctan (\frac{3}{x})) = - \frac{3}{9 + x ^{2}}

= - \frac{9}{81 + x ^{2}} - \frac{3}{9 + x ^{2}}

Vereinfache

- \frac{9}{81 + x ^{2}} - \frac{3}{9 + x ^{2}} : \frac{- 12 x ^{2} - 324}{( x ^{2} + 9 ) ( x ^{2} + 81 )}

= \frac{- 12 x ^{2} - 324}{( x ^{2} + 9 ) ( x ^{2} + 81 )}

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