(\partial)/(\partial z)(xe^y+ye^z+ze^x)

Lösung

\frac{\partial}{\partial z} (x e^{y} + y e^{z} + z e^{x})

e^{z} y + e^{x}

Schritte zur Lösung

\frac{\partial}{\partial z} (x e^{y} + y e^{z} + z e^{x})

Behandle

x, y

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial z} (x e^{y}) + \frac{\partial}{\partial z} (y e^{z}) + \frac{\partial}{\partial z} (z e^{x})

\frac{\partial}{\partial z} (x e^{y}) = 0

\frac{\partial}{\partial z} (y e^{z}) = y e^{z}

\frac{\partial}{\partial z} (z e^{x}) = e^{x}

= 0 + y e^{z} + e^{x}

Vereinfache

= e^{z} y + e^{x}

t an g e n t \frac{2}{4 - x}, at x = 1

\frac{\partial}{\partial y} (4 - x^{2} - y^{2})

\frac{\partial}{\partial x} (6 x^{3} cos (6 x^{2} y))

x \to \infty lim (9^{x})

\frac{d}{d x} (\frac{1}{x ^{10}})