(\partial)/(\partial x)(1+xln(xy-5))

Lösung

\frac{\partial}{\partial x} (1 + x ln (x y - 5))

\frac{x y}{x y - 5} + ln (x y - 5)

Schritte zur Lösung

\frac{\partial}{\partial x} (1 + x ln (x y - 5))

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (1) + \frac{\partial}{\partial x} (x ln (x y - 5))

\frac{\partial}{\partial x} (1) = 0

\frac{\partial}{\partial x} (x ln (x y - 5)) = ln (y x - 5) + \frac{y x}{y x - 5}

= 0 + ln (y x - 5) + \frac{y x}{y x - 5}

Vereinfache

= \frac{x y}{x y - 5} + ln (x y - 5)

\frac{\partial}{\partial x} (π r^{2} h)

\int e^{(x)} d x

\frac{d}{d x} (- 3 cos (2 x))

d er i v a t i v e (3 x^{6} + 2 x^{3})^{4}

\int \frac{( 16 x ^{2} )}{( 2 x + 5 ) ^{5}} d x