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Beliebt Rechnen >

derivative of 1/16 x^4+1/(2x^2)

Lösung

\frac{d}{d x} (\frac{1}{16} x^{4} + \frac{1}{2 x ^{2}})

Lösung

\frac{x ^{3}}{4} - \frac{1}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{16} x^{4} + \frac{1}{2 x ^{2}})

Vereinfache

\frac{1}{16} x^{4} + \frac{1}{2 x ^{2}} : \frac{x ^{4}}{16} + \frac{1}{2 x ^{2}}

= \frac{d}{d x} (\frac{x ^{4}}{16} + \frac{1}{2 x ^{2}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{x ^{4}}{16}) + \frac{d}{d x} (\frac{1}{2 x ^{2}})

\frac{d}{d x} (\frac{x ^{4}}{16}) = \frac{x ^{3}}{4}

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

= \frac{x ^{3}}{4} - \frac{1}{x ^{3}}

Graph

Beliebte Beispiele

limit as x approaches 3 of 2x+3

x \to 3 lim (2 x + 3)

derivative of {r}(x*cos(x))

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derivative of cos(1/(x^2))

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

f (t) = \frac{t}{2}