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Beliebt Rechnen >

(\partial)/(\partial y)(x^2y+y^2z+xz^2)

Lösung

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

Lösung

x^{2} + 2 yz

Schritte zur Lösung

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

Behandle

x, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial y} (y^{2} z) = 2 zy

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

= x^{2} + 2 zy + 0

Vereinfache

= x^{2} + 2 yz

Beliebte Beispiele

derivative f(x)=(6x-1)/(x^3)

integral from 3 to 5 of x^3

integral from 0 to 3 of 1/(x-2)

fläche x,2xsqrt(81-x^2)

integral of 1+cos^2(x)