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Beliebt Rechnen >

derivative y= 2/3 x^3-3/(4x^2)

Lösung

ableitung von

y = \frac{2}{3} x^{3} - \frac{3}{4 x ^{2}}

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (\frac{2}{3} x^{3} - \frac{3}{4 x ^{2}})

Vereinfache

\frac{2}{3} x^{3} - \frac{3}{4 x ^{2}} : \frac{2 x ^{3}}{3} - \frac{3}{4 x ^{2}}

= \frac{d}{d x} (\frac{2 x ^{3}}{3} - \frac{3}{4 x ^{2}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{2 x ^{3}}{3}) - \frac{d}{d x} (\frac{3}{4 x ^{2}})

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

\frac{d}{d x} (\frac{3}{4 x ^{2}}) = - \frac{3}{2 x ^{3}}

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

Vereinfache

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

Graph

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