implicit (dy)/(dx),x^3-3x^2y+2xy^2=12

Lösung

implizite ableitung

\frac{d y}{d x}, x^{3} - 3 x^{2} y + 2 x y^{2} = 12

\frac{d y}{d x} = \frac{- 3 x ^{2} + 6 x y - 2 y ^{2}}{x ( - 3 x + 4 y )}

Schritte zur Lösung

x^{3} - 3 x^{2} y + 2 x y^{2} = 12

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

3 x^{2} - 3 (2 x y + \frac{d y}{d x} x^{2}) + 2 (y^{2} + 2 x y \frac{d y}{d x}) = 0

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 3 x ^{2} + 6 x y - 2 y ^{2}}{x ( - 3 x + 4 y )}

\frac{d y}{d x} = \frac{- 3 x ^{2} + 6 x y - 2 y ^{2}}{x ( - 3 x + 4 y )}

d er i v a t i v e x^{2} (1 - 6 x)

\frac{d}{d x} (x^{5} e^{- 3 l n (x)})

\int sec^{2} (5 x t a) n^{3} 5 x d x

\int cos (x) cos (5 x) d x

a re a f (x) = x^{2}, (1, 5), 5