derivative y=(arctan(3x))^2

Lösung

ableitung von

y = (arctan (3 x))^{2}

\frac{6 arctan ( 3 x )}{9 x ^{2} + 1}

Schritte zur Lösung

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

Wende die Kettenregel an:

2 arctan (3 x) \frac{d}{d x} (arctan (3 x))

= 2 arctan (3 x) \frac{d}{d x} (arctan (3 x))

\frac{d}{d x} (arctan (3 x)) = \frac{3}{9 x ^{2} + 1}

= 2 arctan (3 x) \frac{3}{9 x ^{2} + 1}

Vereinfache

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

= \frac{6 arctan ( 3 x )}{9 x ^{2} + 1}

y^{^{''}} + 9 y^{^{'}} = 5 csc^{2} (3 t)

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