(\partial)/(\partial x)((x+y)ln(xy))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x + y, g = ln (x y)

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

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

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

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

Vereinfache

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

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

x \to 0 lim (\frac{4}{x ^{5}})

\frac{d}{d x} (x^{2} sin (x))

\frac{d}{d x} (e^{k t a n (7 x)})

t an g e n t 5 - x - x^{2}

\int \frac{5 x}{x ( x - 1 )} d x