derivative of arctan(1-3x^2)

Lösung

\frac{d}{d x} (arctan (1 - 3 x^{2}))

- \frac{6 x}{9 x ^{4} - 6 x ^{2} + 2}

Schritte zur Lösung

\frac{d}{d x} (arctan (1 - 3 x^{2}))

Wende die Kettenregel an:

\frac{1}{( 1 - 3 x ^{2} ) ^{2} + 1} \frac{d}{d x} (1 - 3 x^{2})

= \frac{1}{( 1 - 3 x ^{2} ) ^{2} + 1} \frac{d}{d x} (1 - 3 x^{2})

\frac{d}{d x} (1 - 3 x^{2}) = - 6 x

= \frac{1}{( 1 - 3 x ^{2} ) ^{2} + 1} (- 6 x)

Vereinfache

\frac{1}{( 1 - 3 x ^{2} ) ^{2} + 1} (- 6 x) : - \frac{6 x}{9 x ^{4} - 6 x ^{2} + 2}

= - \frac{6 x}{9 x ^{4} - 6 x ^{2} + 2}

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ma c l a u r in sin (5 x) \cdot sin (4 x)

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