derivative ((x^2+8)/(x^2-8))^3

Lösung

ableitung von

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

- \frac{96 x ( x ^{2} + 8 ) ^{2}}{( x ^{2} - 8 ) ^{4}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x ^{2} + 8}{x ^{2} - 8}) = - \frac{32 x}{( x ^{2} - 8 ) ^{2}}

= 3 (\frac{x ^{2} + 8}{x ^{2} - 8})^{2} (- \frac{32 x}{( x ^{2} - 8 ) ^{2}})

Vereinfache

3 (\frac{x ^{2} + 8}{x ^{2} - 8})^{2} (- \frac{32 x}{( x ^{2} - 8 ) ^{2}}) : - \frac{96 x ( x ^{2} + 8 ) ^{2}}{( x ^{2} - 8 ) ^{4}}

= - \frac{96 x ( x ^{2} + 8 ) ^{2}}{( x ^{2} - 8 ) ^{4}}

\int \frac{1}{36 e ^{- 8 x} + e ^{8 x}} d x

\frac{\partial}{\partial x} (z e^{x + y} - x y)

\frac{d}{d x} ((x + 1) (x + 1 - \frac{1}{x + 2}))

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in v erse l a pl a ce \frac{15}{( s + 10 ) ( s + 11 )}