derivative of sqrt((x^2-1/(x^3-x)))

Lösung

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

- \frac{1}{2 x ^{\frac{3}{2}}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - \frac{1}{2 x ^{\frac{3}{2}}}

\int \frac{3 - 6 x}{25 - 9 x ^{2}} d x

\frac{\partial}{\partial x} ((x + y) e^{3 x - 4 y})

\frac{d ^{2}}{d x ^{2}} (\frac{e ^{x}}{8 x + 1})

d er i v a t i v e ln (ln (x^{2}))

n = 1 \sum \infty \frac{4}{1 0 ^{n}}