derivative arctan(7/(x^2))

Lösung

ableitung von

arctan (\frac{7}{x ^{2}})

- \frac{14 x}{49 + x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (arctan (\frac{7}{x ^{2}}))

Wende die Kettenregel an:

\frac{1}{( \frac{7}{x ^{2}} ) ^{2} + 1} \frac{d}{d x} (\frac{7}{x ^{2}})

= \frac{1}{( \frac{7}{x ^{2}} ) ^{2} + 1} \frac{d}{d x} (\frac{7}{x ^{2}})

\frac{d}{d x} (\frac{7}{x ^{2}}) = - \frac{14}{x ^{3}}

= \frac{1}{( \frac{7}{x ^{2}} ) ^{2} + 1} (- \frac{14}{x ^{3}})

Vereinfache

\frac{1}{( \frac{7}{x ^{2}} ) ^{2} + 1} (- \frac{14}{x ^{3}}) : - \frac{14 x}{49 + x ^{4}}

= - \frac{14 x}{49 + x ^{4}}

d er i v a t i v e (3 x + 4) x^{2}

\int 7 (sec (x))^{2} - 4 sin (x) d x

\int x^{2} - \frac{3}{4} d x

\frac{d}{d x} (sin (π))

\frac{d}{d x} ((x^{3} + 2) e^{x})