(\partial)/(\partial z)(x^2y+yz^3+z^5x)

Lösung

\frac{\partial}{\partial z} (x^{2} y + y z^{3} + z^{5} x)

5 x z^{4} + 3 y z^{2}

Schritte zur Lösung

\frac{\partial}{\partial z} (x^{2} y + y z^{3} + z^{5} x)

Behandle

x, y

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial z} (x^{2} y) + \frac{\partial}{\partial z} (y z^{3}) + \frac{\partial}{\partial z} (z^{5} x)

\frac{\partial}{\partial z} (x^{2} y) = 0

\frac{\partial}{\partial z} (y z^{3}) = 3 y z^{2}

\frac{\partial}{\partial z} (z^{5} x) = 5 x z^{4}

= 0 + 3 y z^{2} + 5 x z^{4}

Vereinfache

= 5 x z^{4} + 3 y z^{2}

\int x^{3} 25 + x^{2} d x

x \to 0 lim (\frac{g ( x )}{x})

\frac{d y}{d x} = x e^{x - 2 y}

\int x \cdot ln (2 x) d x

\frac{d}{d x} (2 x^{3} - 21 x^{2} + 60 x)