derivative of arctan(1/(1+x^2))

Lösung

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

- \frac{2 x}{x ^{4} + 2 x ^{2} + 2}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{( \frac{1}{1 + x ^{2}} ) ^{2} + 1} (- \frac{2 x}{( 1 + x ^{2} ) ^{2}}) : - \frac{2 x}{x ^{4} + 2 x ^{2} + 2}

= - \frac{2 x}{x ^{4} + 2 x ^{2} + 2}

\int_{- 5}^{5} 4 (25 - x^{2}) d x

d er i v a t i v e 8 x - 5

\frac{d ^{4}}{d x ^{4}} (ln (1 + x))

y^{^{'}} + x = 0

\int 8 - 4 x - 4 x^{2} d x