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

Lösung

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

- \frac{12 x ( x ^{2} + 1 ) ^{2}}{( x ^{2} - 1 ) ^{4}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x ^{2} + 1}{x ^{2} - 1}) = - \frac{4 x}{( x ^{2} - 1 ) ^{2}}

= 3 (\frac{x ^{2} + 1}{x ^{2} - 1})^{2} (- \frac{4 x}{( x ^{2} - 1 ) ^{2}})

Vereinfache

3 (\frac{x ^{2} + 1}{x ^{2} - 1})^{2} (- \frac{4 x}{( x ^{2} - 1 ) ^{2}}) : - \frac{12 x ( x ^{2} + 1 ) ^{2}}{( x ^{2} - 1 ) ^{4}}

= - \frac{12 x ( x ^{2} + 1 ) ^{2}}{( x ^{2} - 1 ) ^{4}}

\frac{d}{d x} ((x - 6) (5 x + 1))

\frac{\partial ^{2}}{\partial y ^{2}} (\frac{x y}{x - y})

\int \frac{3 + x}{1 - x ^{2}} d x

y = (5 - x^{2})^{5}

t an g e n t f (x) = \frac{1}{x ^{3}}, at x = 1