implicit (dy)/(dx),x^{2/3}+y^{2/3}=3

Lösung

implizite ableitung

\frac{d y}{d x}, x^{\frac{2}{3}} + y^{\frac{2}{3}} = 3

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

Schritte zur Lösung

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

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

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

Isoliere

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

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

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