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Beliebt Rechnen >

(\partial)/(\partial y)(4xln(xy))

Lösung

\frac{\partial}{\partial y} (4 x ln (x y))

Lösung

\frac{4 x}{y}

Schritte zur Lösung

\frac{\partial}{\partial y} (4 x ln (x y))

Behandle

x

als Konstante

Entferne die Konstante:

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

= 4 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

= 4 x \frac{1}{x y} x

Vereinfache

4 x \frac{1}{x y} x : \frac{4 x}{y}

= \frac{4 x}{y}

Beliebte Beispiele

(dy)/(dt)+1/t y= 6/t ,y(1)=6

\frac{d y}{d t} + \frac{1}{t} y = \frac{6}{t}, y (1) = 6

integral of (sin(x/2))/(cos^2(x/2))

\int \frac{sin ( \frac{x}{2} )}{cos ^{2} ( \frac{x}{2} )} d x

derivative f(x)=2x-6

d er i v a t i v e f (x) = 2 x - 6

d/(dt)(e^t+e^{-t})

\frac{d}{d t} (e^{t} + e^{- t})

limit as x approaches 3 of (x+4)/(x-2)

x \to 3 lim (\frac{x + 4}{x - 2})