(\partial)/(\partial x)(xyln(xy))

Lösung

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

y (ln (x y) + 1)

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = ln (x y)

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

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (ln (x y)) = \frac{1}{x}

= y (1 \cdot ln (x y) + \frac{1}{x} x)

Vereinfache

y (1 \cdot ln (x y) + \frac{1}{x} x) : y (ln (x y) + 1)

= y (ln (x y) + 1)

\frac{x d y}{d x} = - y + 2 x^{2} y, y (1) = 1

y \to 2 lim (4 y^{2} - 2 y)

\int_{0}^{- 0.3} 300 x d x

t an g e n t f (x) = e^{2 x}, at x = \frac{1}{2} ln (3)

x \to 3 lim (2 x + ∣ x - 3 ∣)