(\partial)/(\partial x)(2x^3+2y^2-12xy+10)

Lösung

\frac{\partial}{\partial x} (2 x^{3} + 2 y^{2} - 12 x y + 10)

6 x^{2} - 12 y

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x^{3} + 2 y^{2} - 12 x y + 10)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (2 x^{3}) + \frac{\partial}{\partial x} (2 y^{2}) - \frac{\partial}{\partial x} (12 x y) + \frac{\partial}{\partial x} (10)

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

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

\frac{\partial}{\partial x} (12 x y) = 12 y

\frac{\partial}{\partial x} (10) = 0

= 6 x^{2} + 0 - 12 y + 0

Vereinfache

= 6 x^{2} - 12 y

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

\int_{0}^{120} 5.5 (120 - x) d x

\frac{d}{d x} (cos^{2} (x^{3}))

\int_{0}^{x} 1 + x^{2} d x

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