(\partial)/(\partial y)(3x^2y^4+1)

Lösung

\frac{\partial}{\partial y} (3 x^{2} y^{4} + 1)

12 x^{2} y^{3}

Schritte zur Lösung

\frac{\partial}{\partial y} (3 x^{2} y^{4} + 1)

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (3 x^{2} y^{4}) + \frac{\partial}{\partial y} (1)

\frac{\partial}{\partial y} (3 x^{2} y^{4}) = 12 x^{2} y^{3}

\frac{\partial}{\partial y} (1) = 0

= 12 x^{2} y^{3} + 0

Vereinfache

= 12 x^{2} y^{3}

\frac{\partial}{\partial x} (4 x^{3} y^{2} - 4 x^{2} + y^{6} + 1)

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