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

Lösung

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

- \frac{48}{x ^{3}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} ((\frac{x + 2}{x})^{3}) = - \frac{6 ( x + 2 ) ^{2}}{x ^{4}}

\frac{d}{d x} ((\frac{x - 2}{x})^{3}) = \frac{6 ( x - 2 ) ^{2}}{x ^{4}}

= - \frac{6 ( x + 2 ) ^{2}}{x ^{4}} + \frac{6 ( x - 2 ) ^{2}}{x ^{4}}

Vereinfache

- \frac{6 ( x + 2 ) ^{2}}{x ^{4}} + \frac{6 ( x - 2 ) ^{2}}{x ^{4}} : - \frac{48}{x ^{3}}

= - \frac{48}{x ^{3}}

\frac{d x}{d y} - \frac{x}{y} = 2 y

\frac{d}{d x} y = 24 x

x \to 0 lim (2 x sin (\frac{1}{x}))

y^{^{'}} = \frac{e ^{y} + 1}{e ^{y}}

x \to 3 lim (x^{3} + 3 x^{2} - x + 2)