implicit (dy)/(dx),3xy+1=0

Lösung

implizite ableitung

\frac{d y}{d x}, 3 x y + 1 = 0

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

Schritte zur Lösung

3 x y + 1 = 0

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

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

Isoliere

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

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

\int_{0}^{33} 3 (x - 1)^{- \frac{1}{5}} d x

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

\int 5 x^{\frac{1}{2}} d x

\frac{\partial}{\partial y} (\frac{x ^{2} - y ^{2}}{x y})

\int \frac{2 x}{x ^{2} + 5} d x