derivative of ((x+4/(x-4))^5)

Lösung

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

- \frac{40 ( x + 4 ) ^{4}}{( x - 4 ) ^{6}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

5 (\frac{x + 4}{x - 4})^{4} (- \frac{8}{( x - 4 ) ^{2}}) : - \frac{40 ( x + 4 ) ^{4}}{( x - 4 ) ^{6}}

= - \frac{40 ( x + 4 ) ^{4}}{( x - 4 ) ^{6}}

\frac{d}{d x} (8 sin (x) - x)

\int e^{- x y} sin (x) d x

\int x sin (3 x + 1) d x

in v erse l a pl a ce \frac{e ^{- π s}}{s ^{3} + s}

y^{^{'}} = 0.5 x - 450