derivative ((x^2+2)/(x^2-2))^4

Lösung

ableitung von

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

- \frac{32 x ( x ^{2} + 2 ) ^{3}}{( x ^{2} - 2 ) ^{5}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

= 4 (\frac{x ^{2} + 2}{x ^{2} - 2})^{3} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}})

Vereinfache

4 (\frac{x ^{2} + 2}{x ^{2} - 2})^{3} (- \frac{8 x}{( x ^{2} - 2 ) ^{2}}) : - \frac{32 x ( x ^{2} + 2 ) ^{3}}{( x ^{2} - 2 ) ^{5}}

= - \frac{32 x ( x ^{2} + 2 ) ^{3}}{( x ^{2} - 2 ) ^{5}}

d er i v a t i v e \frac{1}{( 3 x + 1 )}

a re a y = sin (x), y = cos (x)

l a pl a ce t r an s f or m (e^{, at})

\int x + 4 d x

\int p^{2} ln (p) d p