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Beliebt Rechnen >

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

Lösung

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

Lösung

3 x^{2} + 8 x y

Schritte zur Lösung

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

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

\frac{\partial}{\partial x} (4 x^{2} y) = 8 y x

\frac{\partial}{\partial x} (2 y^{3}) = 0

= 3 x^{2} + 8 y x + 0

Vereinfache

= 3 x^{2} + 8 x y

Beliebte Beispiele

tangent f(x)= 2/(x-1),(3,1)

d/(dy)(1/3 sqrt(y)(y-3))

derivative of x^{ln(x^2+1})

(d^2)/(dx^2)(e^{sin(x)})

derivative of (sin(y)x^2)