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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{x}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

= \frac{1}{x y} y

Vereinfache

\frac{1}{x y} y : \frac{1}{x}

= \frac{1}{x}

Beliebte Beispiele

limit as x approaches 9 of x+7

x \to 9 lim (x + 7)

d/(dt)(10^{2sqrt(t)})

\frac{d}{d t} (1 0^{2 t})

derivative y=x^{2/5}(x+3)

d er i v a t i v e y = x^{\frac{2}{5}} (x + 3)

derivative of (x^3-4/(x-1))

\frac{d}{d x} (\frac{x ^{3} - 4}{x - 1})

integral of (3x-2)/(x+1)

\int \frac{3 x - 2}{x + 1} d x