d/(d{r)}(-arctan({r})+2arccot({r})-ln({r}))

Lösung

\frac{d}{d r} (- arctan (r) + 2 arccot (r) - ln (r))

- \frac{3}{r ^{2} + 1} - \frac{1}{r}

Schritte zur Lösung

\frac{d}{d r} (- arctan (r) + 2 arccot (r) - ln (r))

Wende die Summen-/Differenzregel an:

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

= - \frac{d}{d r} (arctan (r)) + \frac{d}{d r} (2 arccot (r)) - \frac{d}{d r} (ln (r))

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

\frac{d}{d r} (2 arccot (r)) = - \frac{2}{r ^{2} + 1}

\frac{d}{d r} (ln (r)) = \frac{1}{r}

= - \frac{1}{r ^{2} + 1} - \frac{2}{r ^{2} + 1} - \frac{1}{r}

Ziehe Brüche zusammen

- \frac{1}{r ^{2} + 1} - \frac{2}{r ^{2} + 1} : - \frac{3}{r ^{2} + 1}

= - \frac{3}{r ^{2} + 1} - \frac{1}{r}

\int 19 d x

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