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Beliebt Rechnen >

implicit 2xy-y^2=-1

Lösung

implizite ableitung

2 x y - y^{2} = - 1

Lösung

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

Schritte zur Lösung

2 x y - y^{2} = - 1

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

2 (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{y}{x - y}

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

Beliebte Beispiele

integral of (3x^2+4x-6)

\int (3 x^{2} + 4 x - 6) d x

derivative of-1/3 (x^{-3}-x^6)

\frac{d}{d x} (- \frac{1}{3} (x^{- 3} - x^{6}))

(\partial)/(\partial x)(xcos(xy)-2y)

\frac{\partial}{\partial x} (x cos (x y) - 2 y)

derivative of cos(xsec^7(x))

\frac{d}{d x} (cos (x) sec^{7} (x))

integral of 3sin^3(xco)s^2x

\int 3 sin^{3} (x co) s^{2} x d x