derivative of (x-1/x ^2)

Lösung

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

2 x - \frac{2}{x ^{3}}

Schritte zur Lösung

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

Vereinfache

(x - \frac{1}{x})^{2} : x^{2} - 2 + \frac{1}{x ^{2}}

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (2) = 0

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

= 2 x - 0 - \frac{2}{x ^{3}}

Vereinfache

= 2 x - \frac{2}{x ^{3}}

t \to \frac{x}{2} lim (\frac{sin ( t )}{t})

s l o p e (- 3.5) (4.3)

\frac{\partial}{\partial x} (- \frac{x}{y ^{2}})

in v erse l a pl a ce \frac{s + 2}{s ^{2} + 2 s + 2}

x \to - 4 lim (7 - x)