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Beliebt Rechnen >

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

Lösung

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

Lösung

x^{2} + 6 x y

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

\frac{\partial}{\partial y} (3 x y^{2}) = 6 x y

= 0 + x^{2} + 6 x y

Vereinfache

= x^{2} + 6 x y

Beliebte Beispiele

steigung y=x^2+3

integral of (7x)/(e^{x^2)}

integral of 1/(x^3)+6/(x^7)

sum from n=0 to infinity of 1/((2+2n)^3)

integral from-1 to 3 of 2x^2+8