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Beliebt Rechnen >

implicit (dy)/(dx),4x^2+5xy-y^2=2

Lösung

implizite ableitung

\frac{d y}{d x}, 4 x^{2} + 5 x y - y^{2} = 2

Lösung

\frac{d y}{d x} = \frac{- 8 x - 5 y}{5 x - 2 y}

Schritte zur Lösung

4 x^{2} + 5 x y - y^{2} = 2

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

8 x + 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{- 8 x - 5 y}{5 x - 2 y}

\frac{d y}{d x} = \frac{- 8 x - 5 y}{5 x - 2 y}

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x*(dy)/(dx)-x^2+x*e^{-x}=0

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