implicit (dy)/(dx),x^2-xy+y^2=19

Lösung

implizite ableitung

\frac{d y}{d x}, x^{2} - x y + y^{2} = 19

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

Schritte zur Lösung

x^{2} - x y + y^{2} = 19

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

2 x - 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{- 2 x + y}{- x + 2 y}

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

\frac{\partial}{\partial x} (\frac{5 s - 3 t}{4 s + 5 t})

x \to 0 - lim (\frac{7 e ^{x}}{x ^{5}})

\frac{d y}{d x} = \frac{x y + 3 x - y - 3}{x y - 2 x + 4 y - 8}

(3 ln (x))^{^{'}}

\frac{d}{d x} (sin (\frac{1}{x ^{2} - 5}))