derivative arctan(sqrt(5x^2-1))

Lösung

ableitung von

arctan (5 x^{2} - 1)

\frac{1}{x 5 x ^{2} - 1}

Schritte zur Lösung

\frac{d}{d x} (arctan (5 x^{2} - 1))

Wende die Kettenregel an:

\frac{1}{( 5 x ^{2} - 1 ) ^{2} + 1} \frac{d}{d x} (5 x^{2} - 1)

= \frac{1}{( 5 x ^{2} - 1 ) ^{2} + 1} \frac{d}{d x} (5 x^{2} - 1)

\frac{d}{d x} (5 x^{2} - 1) = \frac{5 x}{5 x ^{2} - 1}

= \frac{1}{( 5 x ^{2} - 1 ) ^{2} + 1} \cdot \frac{5 x}{5 x ^{2} - 1}

Vereinfache

\frac{1}{( 5 x ^{2} - 1 ) ^{2} + 1} \cdot \frac{5 x}{5 x ^{2} - 1} : \frac{1}{x 5 x ^{2} - 1}

= \frac{1}{x 5 x ^{2} - 1}

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