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Beliebt Rechnen >

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

Lösung

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

Lösung

12 x^{2} + 2 y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

Vereinfache

= 12 x^{2} + 2 y

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