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Beliebt Rechnen >

implicit (dy)/(dx),x+y=xy

Lösung

implizite ableitung

\frac{d y}{d x}, x + y = x y

Lösung

\frac{d y}{d x} = \frac{y - 1}{1 - x}

Schritte zur Lösung

x + y = x y

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

1 + \frac{d y}{d x} = y + x \frac{d y}{d x}

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{y - 1}{1 - x}

\frac{d y}{d x} = \frac{y - 1}{1 - x}

Beliebte Beispiele

derivative of 2x^2-1/x

\frac{d}{d x} (2 x^{2} - \frac{1}{x})

integral from 0 to 8 of 1

\int_{0}^{8} 1

limit as x approaches 3 of x^2-4x+10

x \to 3 lim (x^{2} - 4 x + 10)

integral of tan^3(5x)sec(5x)

\int tan^{3} (5 x) sec (5 x) d x

integral of (x-1)/(x^2+x-6)

\int \frac{x - 1}{x ^{2} + x - 6} d x