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Beliebt Rechnen >

implicit (dy)/(dx),50x^{1/3}y^{2/3}=600

Lösung

implizite ableitung

\frac{d y}{d x}, 50 x^{\frac{1}{3}} y^{\frac{2}{3}} = 600

Lösung

\frac{d y}{d x} = - \frac{y}{2 x}

Schritte zur Lösung

50 x^{\frac{1}{3}} y^{\frac{2}{3}} = 600

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

\frac{50 ( y + 2 x \frac{d y}{d x} )}{3 x ^{\frac{2}{3}} y ^{\frac{1}{3}}} = 0

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y}{2 x}

\frac{d y}{d x} = - \frac{y}{2 x}

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