derivative of arcsin((x^2-1/(x^2)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e f (x) = \frac{3}{x ^{7}}

\int 2 t d t

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

\frac{d y}{d x} = x y + x + y + 1

\frac{\partial}{\partial y} (x^{2} \cdot y^{3})