derivative of ((x+9/(x-9))^5)

Lösung

\frac{d}{d x} ((\frac{x + 9}{x - 9})^{5})

- \frac{90 ( x + 9 ) ^{4}}{( x - 9 ) ^{6}}

Schritte zur Lösung

\frac{d}{d x} ((\frac{x + 9}{x - 9})^{5})

Wende die Kettenregel an:

5 (\frac{x + 9}{x - 9})^{4} \frac{d}{d x} (\frac{x + 9}{x - 9})

= 5 (\frac{x + 9}{x - 9})^{4} \frac{d}{d x} (\frac{x + 9}{x - 9})

\frac{d}{d x} (\frac{x + 9}{x - 9}) = - \frac{18}{( x - 9 ) ^{2}}

= 5 (\frac{x + 9}{x - 9})^{4} (- \frac{18}{( x - 9 ) ^{2}})

Vereinfache

5 (\frac{x + 9}{x - 9})^{4} (- \frac{18}{( x - 9 ) ^{2}}) : - \frac{90 ( x + 9 ) ^{4}}{( x - 9 ) ^{6}}

= - \frac{90 ( x + 9 ) ^{4}}{( x - 9 ) ^{6}}

x \to - 6 - lim (\frac{x + 2}{x + 6})

\int \frac{9}{x ^{2} - 9 x} d x

t a y l or \frac{x}{1 + x ^{2}}

\int a x^{2} d x

d er i v a t i v e 5 - (x - 9)^{4}