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

Lösung

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

- 6 z x

Schritte zur Lösung

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

Behandle

z, y

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (2 z^{3}) = 0

\frac{\partial}{\partial x} (3 (x^{2} + y^{2}) z) = 6 z x

= 0 - 6 z x

Vereinfache

= - 6 z x

x \to - 8 + lim (\frac{x}{x + 8})

\frac{\partial}{\partial x} (6 x^{3} y + 6 y^{5} + 1)

\int_{1}^{R} x^{- \frac{7}{5}} d x

\frac{d}{d x} ((6 x^{5} - 4 x^{4} + 7 x) (x^{3} - x^{2} - 1))

\frac{\partial}{\partial x} (e^{x + y + 5})