derivative y=((x^2+3)/(x^2-3))^7

Lösung

ableitung von

y = (\frac{x ^{2} + 3}{x ^{2} - 3})^{7}

- \frac{84 x ( x ^{2} + 3 ) ^{6}}{( x ^{2} - 3 ) ^{8}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x ^{2} + 3}{x ^{2} - 3})^{7})

Wende die Kettenregel an:

7 (\frac{x ^{2} + 3}{x ^{2} - 3})^{6} \frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3})

= 7 (\frac{x ^{2} + 3}{x ^{2} - 3})^{6} \frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3})

\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 3}) = - \frac{12 x}{( x ^{2} - 3 ) ^{2}}

= 7 (\frac{x ^{2} + 3}{x ^{2} - 3})^{6} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}})

Vereinfache

7 (\frac{x ^{2} + 3}{x ^{2} - 3})^{6} (- \frac{12 x}{( x ^{2} - 3 ) ^{2}}) : - \frac{84 x ( x ^{2} + 3 ) ^{6}}{( x ^{2} - 3 ) ^{8}}

= - \frac{84 x ( x ^{2} + 3 ) ^{6}}{( x ^{2} - 3 ) ^{8}}

x \to 2 lim (x^{2} + 5 x - 9)

d er i v a t i v e y = 3 tan (3 t)

p a r i t y cot^{2} (cos (θ))

\frac{d}{d x} (arcsin (6 x^{4}))

\frac{d}{d x} (\frac{x ^{2}}{3} + \frac{5 x}{7} - \frac{8}{5})