derivative of arccsc(-x^2)

Lösung

\frac{d}{d x} (arccsc (- x^{2}))

\frac{2}{x x ^{4} - 1}

Schritte zur Lösung

\frac{d}{d x} (arccsc (- x^{2}))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

- \frac{1}{( - x ^{2} ) ^{2} ( - x ^{2} ) ^{2} - 1} (- 2 x) : \frac{2}{x x ^{4} - 1}

= \frac{2}{x x ^{4} - 1}

\int \frac{tan ^{2} ( x )}{2 sec ( x )} d x

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\frac{\partial}{\partial x} (- \frac{x}{y})