(\partial)/(\partial x)(7+xln(xy-9))

Lösung

\frac{\partial}{\partial x} (7 + x ln (x y - 9))

\frac{x y}{x y - 9} + ln (x y - 9)

Schritte zur Lösung

\frac{\partial}{\partial x} (7 + x ln (x y - 9))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (7) + \frac{\partial}{\partial x} (x ln (x y - 9))

\frac{\partial}{\partial x} (7) = 0

\frac{\partial}{\partial x} (x ln (x y - 9)) = ln (y x - 9) + \frac{y x}{y x - 9}

= 0 + ln (y x - 9) + \frac{y x}{y x - 9}

Vereinfache

= \frac{x y}{x y - 9} + ln (x y - 9)

\frac{d}{d x} ((x^{3} + 5 x^{2} - x^{- 2} + 8)^{- \frac{7}{6}})

q \to 0 + lim (4 q)

\int 22 x^{21} d x

x \to 8 lim (x^{\frac{8}{3}})

(2 x - x^{- 2} y) d x + x^{- 1} d y = 0