(\partial)/(\partial x)(6+xln(xy-9))

Lösung

\frac{\partial}{\partial x} (6 + x ln (x y - 9))

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

Schritte zur Lösung

\frac{\partial}{\partial x} (6 + x ln (x y - 9))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (6) + \frac{\partial}{\partial x} (x ln (x y - 9))

\frac{\partial}{\partial x} (6) = 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)

d er i v a t i v e f (x) = x^{2} - 3 x + 2

in v erse l a pl a ce \frac{s + 1}{( s - 1 ) \cdot ( s - 2 )}

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

\frac{d}{d x} ((x + 1)^{5})

d er i v a t i v e t^{3} sin (t)