derivative ((x^2+1)/(x^2-1))^7

Lösung

ableitung von

(\frac{x ^{2} + 1}{x ^{2} - 1})^{7}

- \frac{28 x ( x ^{2} + 1 ) ^{6}}{( x ^{2} - 1 ) ^{8}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x ^{2} + 1}{x ^{2} - 1})^{7})

Wende die Kettenregel an:

7 (\frac{x ^{2} + 1}{x ^{2} - 1})^{6} \frac{d}{d x} (\frac{x ^{2} + 1}{x ^{2} - 1})

= 7 (\frac{x ^{2} + 1}{x ^{2} - 1})^{6} \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}}

= 7 (\frac{x ^{2} + 1}{x ^{2} - 1})^{6} (- \frac{4 x}{( x ^{2} - 1 ) ^{2}})

Vereinfache

7 (\frac{x ^{2} + 1}{x ^{2} - 1})^{6} (- \frac{4 x}{( x ^{2} - 1 ) ^{2}}) : - \frac{28 x ( x ^{2} + 1 ) ^{6}}{( x ^{2} - 1 ) ^{8}}

= - \frac{28 x ( x ^{2} + 1 ) ^{6}}{( x ^{2} - 1 ) ^{8}}

\frac{d}{d x} ((x^{3} - 3 x) (2 x^{2} + 3 x + 5))

n = 0 \sum \infty \frac{1}{3 ^{n}}

f (x) = 7 ln (x)

\int \frac{15}{25 + x ^{2}} d x

x \to - 2 lim (\frac{2}{x + 2})