derivative 1/6 x^3+1/(2x)

Lösung

ableitung von

\frac{1}{6} x^{3} + \frac{1}{2 x}

\frac{x ^{2}}{2} - \frac{1}{2 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{6} x^{3} + \frac{1}{2 x})

Vereinfache

\frac{1}{6} x^{3} + \frac{1}{2 x} : \frac{x ^{3}}{6} + \frac{1}{2 x}

= \frac{d}{d x} (\frac{x ^{3}}{6} + \frac{1}{2 x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{x ^{3}}{6}) + \frac{d}{d x} (\frac{1}{2 x})

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

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

= \frac{x ^{2}}{2} - \frac{1}{2 x ^{2}}

\frac{d}{d x} (4 + 3 f (x))

l a pl a ce t r an s f or m e^{4 t}

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

x \to 4 + lim (4 x - 4)

\frac{\partial}{\partial x} (e^{3 x} sin (3 y))