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Beliebt Rechnen >

derivative xy^2-x^2y-2=0

Lösung

ableitung von

x y^{2} - x^{2} y - 2 = 0

Lösung

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

Schritte zur Lösung

x y^{2} - x^{2} y - 2 = 0

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

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

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- y ^{2} + 2 x y}{x ( - x + 2 y )}

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

Beliebte Beispiele

derivative r=(t^4+12)(t^6+8)

d er i v a t i v e r = (t^{4} + 12) (t^{6} + 8)

derivative 3x^3y^2=17

d er i v a t i v e 3 x^{3} y^{2} = 17

derivative x^2y+y^2x=6

d er i v a t i v e x^{2} y + y^{2} x = 6

derivative x(x+i)+y(y-i)+i=13

d er i v a t i v e x (x + i) + y (y - i) + i = 13

derivative x^2=2+t

d er i v a t i v e x^{2} = 2 + t