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Beliebt Rechnen >

implicit (dy)/(dx),2x^3-5xy-y^2=3

Lösung

implizite ableitung

\frac{d y}{d x}, 2 x^{3} - 5 x y - y^{2} = 3

Lösung

\frac{d y}{d x} = - \frac{- 6 x ^{2} + 5 y}{2 y + 5 x}

Schritte zur Lösung

2 x^{3} - 5 x y - y^{2} = 3

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

6 x^{2} - 5 (y + x \frac{d y}{d x}) - 2 y \frac{d y}{d x} = 0

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{- 6 x ^{2} + 5 y}{2 y + 5 x}

\frac{d y}{d x} = - \frac{- 6 x ^{2} + 5 y}{2 y + 5 x}

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limit as x approaches-2 of (6x+1)(2x-3)

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