derivative y=((x^2+2)/(x^2-2))^8

Lösung

ableitung von

y = (\frac{x ^{2} + 2}{x ^{2} - 2})^{8}

- \frac{64 x ( x ^{2} + 2 ) ^{7}}{( x ^{2} - 2 ) ^{9}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

= 8 (\frac{x ^{2} + 2}{x ^{2} - 2})^{7} \frac{d}{d x} (\frac{x ^{2} + 2}{x ^{2} - 2})

\frac{d}{d x} (\frac{x ^{2} + 2}{x ^{2} - 2}) = - \frac{8 x}{( x ^{2} - 2 ) ^{2}}

= 8 (\frac{x ^{2} + 2}{x ^{2} - 2})^{7} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}})

Vereinfache

8 (\frac{x ^{2} + 2}{x ^{2} - 2})^{7} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}}) : - \frac{64 x ( x ^{2} + 2 ) ^{7}}{( x ^{2} - 2 ) ^{9}}

= - \frac{64 x ( x ^{2} + 2 ) ^{7}}{( x ^{2} - 2 ) ^{9}}

\int cot (a x) d x

\int e^{\frac{1}{50} x} d x

\frac{d y}{d x} = - 5 y x

\int_{0}^{4} 1 + x d x

\int \frac{- 1}{1 - x} d x