derivative of ((x+8/(x-8))^5)

Lösung

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

- \frac{80 ( x + 8 ) ^{4}}{( x - 8 ) ^{6}}

Schritte zur Lösung

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

Wende die Kettenregel an:

5 (\frac{x + 8}{x - 8})^{4} \frac{d}{d x} (\frac{x + 8}{x - 8})

= 5 (\frac{x + 8}{x - 8})^{4} \frac{d}{d x} (\frac{x + 8}{x - 8})

\frac{d}{d x} (\frac{x + 8}{x - 8}) = - \frac{16}{( x - 8 ) ^{2}}

= 5 (\frac{x + 8}{x - 8})^{4} (- \frac{16}{( x - 8 ) ^{2}})

Vereinfache

5 (\frac{x + 8}{x - 8})^{4} (- \frac{16}{( x - 8 ) ^{2}}) : - \frac{80 ( x + 8 ) ^{4}}{( x - 8 ) ^{6}}

= - \frac{80 ( x + 8 ) ^{4}}{( x - 8 ) ^{6}}

j o in 1 + (\frac{a}{x ^{2}})

x \to 0 lim (\frac{f ( x )}{x ^{2}})

l a pl a ce t r an s f or m e^{- 2 t} t^{2}

\int_{1}^{\infty} x^{2} ln (x) d x

\frac{d}{d x} (\frac{3 x ^{2}}{1 + x ^{3}})