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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

a re a y = 7 x, y = x^{2}

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

x \to 2 + lim (f (x))

\int \frac{21}{4 + 25 x ^{2}} d x