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Beliebt Rechnen >

(\partial)/(\partial x)(z^3ln(xy))

Lösung

\frac{\partial}{\partial x} (z^{3} ln (x y))

Lösung

\frac{z ^{3}}{x}

Schritte zur Lösung

\frac{\partial}{\partial x} (z^{3} ln (x y))

Behandle

z, y

als Konstanten

Entferne die Konstante:

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

= z^{3} \frac{\partial}{\partial x} (ln (x y))

Wende die Kettenregel an:

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

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

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

= z^{3} \frac{1}{x y} y

Vereinfache

z^{3} \frac{1}{x y} y : \frac{z ^{3}}{x}

= \frac{z ^{3}}{x}

Beliebte Beispiele

derivative f(x)=-2x^2-5x+2

d er i v a t i v e f (x) = - 2 x^{2} - 5 x + 2

integral from 0 to 2 of 4^{-θ}

\int_{0}^{2} 4^{- θ} d θ

integral of (3x^2-1)

\int (3 x^{2} - 1) d x

derivative f(x)=2x^3+4x^2+6x

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

limit as x approaches 0+of sin((5pi)/6 e^{sqrt(x)})

x \to 0 + lim (sin (\frac{5 π}{6} e^{x}))