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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

Vereinfache

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

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

\int arcsin (y) d y

\frac{d}{d x} (ln (5 x + 1))

d er i v a t i v e e^{9 x}

im pl i c i t \frac{d y}{d x}, x y = 9 + x^{2} y

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