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

Lösung

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

4 y^{3} + 9 x^{2} y^{2}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{\partial}{\partial y} (3 x^{2} y^{3}) = 9 x^{2} y^{2}

= 0 + 4 y^{3} + 9 x^{2} y^{2}

Vereinfache

= 4 y^{3} + 9 x^{2} y^{2}