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Beliebt Rechnen >

derivative f(x)=arccsc(3x)

Lösung

ableitung von

f (x) = arccsc (3 x)

Lösung

- \frac{1}{x ^{2} 9 x ^{2} - 1}

Schritte zur Lösung

\frac{d}{d x} (arccsc (3 x))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

- \frac{1}{( 3 x ) ^{2} ( 3 x ) ^{2} - 1} \cdot 3 : - \frac{1}{x ^{2} 9 x ^{2} - 1}

= - \frac{1}{x ^{2} 9 x ^{2} - 1}

Graph

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