(\partial)/(\partial x)(x^3+x^2y-4y^3)

Lösung

\frac{\partial}{\partial x} (x^{3} + x^{2} y - 4 y^{3})

3 x^{2} + 2 x y

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{3} + x^{2} y - 4 y^{3})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{3}) + \frac{\partial}{\partial x} (x^{2} y) - \frac{\partial}{\partial x} (4 y^{3})

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

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

\frac{\partial}{\partial x} (4 y^{3}) = 0

= 3 x^{2} + 2 y x - 0

Vereinfache

= 3 x^{2} + 2 x y