derivative of x^3-1/x

Lösung

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

3 x^{2} + \frac{1}{x ^{2}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

= 3 x^{2} + \frac{1}{x ^{2}}

x \to 0 lim (x cos (x^{2}))

\int x \cdot (x^{2} + 1)^{2} d x

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

\int_{0}^{π} cos^{4} (x) sin (x) d x

\frac{\partial}{\partial y} (x + 2 y - 6)