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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= \frac{3 x ^{2}}{2} - \frac{1}{6 x ^{2}}

Graph

Beliebte Beispiele

(\partial)/(\partial x)(3^4-65^3)

\frac{\partial}{\partial x} (3^{4} - 6 5^{3})

y^{^{'}} = 3 y - 2 x

fläche 5cos(7x),5-5cos(7x),[0, pi/7 ]

a re a 5 cos (7 x), 5 - 5 cos (7 x), [0, \frac{π}{7}]

y^'+y/(6.96)=0.0025862069

y^{^{'}} + \frac{y}{6.96} = 0.0025862069

derivative of ln(x^{1/5})

\frac{d}{d x} (ln (x^{\frac{1}{5}}))