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Beliebt Rechnen >

(arcsin((2x)/(1+x^2)))^'

Lösung

(arcsin (\frac{2 x}{1 + x ^{2}}))^{^{'}}

Lösung

- \frac{2}{x ^{2} + 1}

Schritte zur Lösung

(arcsin (\frac{2 x}{1 + x ^{2}}))^{'}

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

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