(\partial)/(\partial y)(5xln(xy))

Lösung

\frac{\partial}{\partial y} (5 x ln (x y))

\frac{5 x}{y}

Schritte zur Lösung

\frac{\partial}{\partial y} (5 x ln (x y))

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

= 5 x \frac{1}{x y} x

Vereinfache

5 x \frac{1}{x y} x : \frac{5 x}{y}

= \frac{5 x}{y}

\frac{\partial}{\partial x} (y^{2} cos (x))

\frac{\partial}{\partial x} (sin (9 x + yz))

\frac{d}{d x} (\frac{x ^{3} - 2 x + 4}{x ^{3}})

\int x (5 x - 3)^{2} d x

\int e^{3 x} + \frac{1}{x} d x