(\partial)/(\partial x)(2+xln(xy-7))

Lösung

\frac{\partial}{\partial x} (2 + x ln (x y - 7))

\frac{x y}{x y - 7} + ln (x y - 7)

Schritte zur Lösung

\frac{\partial}{\partial x} (2 + x ln (x y - 7))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (2) + \frac{\partial}{\partial x} (x ln (x y - 7))

\frac{\partial}{\partial x} (2) = 0

\frac{\partial}{\partial x} (x ln (x y - 7)) = ln (y x - 7) + \frac{y x}{y x - 7}

= 0 + ln (y x - 7) + \frac{y x}{y x - 7}

Vereinfache

= \frac{x y}{x y - 7} + ln (x y - 7)

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