(\partial)/(\partial x)(2xy+xf(x,y)(y/x))

Lösung

\frac{\partial}{\partial x} (2 x y + x f (x, y) (\frac{y}{x}))

2 y + y (1 \cdot f (x, y) \frac{1}{x} + (\frac{\partial}{\partial x} (f (x, y)) \frac{1}{x} + (- \frac{1}{x ^{2}}) f (x, y)) x)

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x y + x f (x, y) (\frac{y}{x}))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (2 x y) + \frac{\partial}{\partial x} (x f (x, y) \frac{y}{x})

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

\frac{\partial}{\partial x} (x f (x, y) \frac{y}{x}) = y (1 \cdot f (x, y) \frac{1}{x} + (\frac{\partial}{\partial x} (f (x, y)) \frac{1}{x} + (- \frac{1}{x ^{2}}) f (x, y)) x)

= 2 y + y (1 \cdot f (x, y) \frac{1}{x} + (\frac{\partial}{\partial x} (f (x, y)) \frac{1}{x} + (- \frac{1}{x ^{2}}) f (x, y)) x)

\frac{\partial}{\partial y} (3 + 2 x y)

a re a 5 x, 3 x^{2}

\frac{\partial}{\partial x} (2 cos (x^{2} + y^{2}))

\frac{d}{d x} (x + 13)

x \to \infty lim (ln ∣ x ∣)