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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\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}

\int \frac{3}{3 x} d x

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\frac{\partial}{\partial x} (3 x^{3} + y^{3})