derivative y^3-3xy^2=x^3+3x^2y

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

3 y^{2} \frac{d y}{d x} - 3 (y^{2} + 2 x y \frac{d y}{d x}) = 3 x^{2} + 3 (2 x y + \frac{d y}{d x} x^{2})

Isoliere

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

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

d er i v a t i v e x^{3} + 3 x^{4} y = 4 y^{2} - 9

d er i v a t i v e ln (x^{6} + y^{20}) = sin (x) + e^{y}

d er i v a t i v e x y^{2} - x^{2} y - 2 = 0

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

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