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

Lösung

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

\frac{y - 2 x}{y}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{y} \frac{\partial}{\partial x} (x y - x^{2})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{1}{y} (\frac{\partial}{\partial x} (x y) - \frac{\partial}{\partial x} (x^{2}))

\frac{\partial}{\partial x} (x y) = y

\frac{\partial}{\partial x} (x^{2}) = 2 x

= \frac{1}{y} (y - 2 x)

Vereinfache

\frac{1}{y} (y - 2 x) : \frac{y - 2 x}{y}

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

l a pl a ce t r an s f or m g (t) = 3 + t^{5} + sin (π t)

\int \frac{1}{3 + 3 2 t ^{2}} d t

d er i v a t i v e x^{3} (x - 6)^{2}

\int x ln (x^{3}) d x

\frac{\partial}{\partial x} (\frac{2 x - y}{x + 4 y})