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Beliebt Rechnen >

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

Lösung

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

Lösung

12 x^{3} y^{2}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial y} (3) = 0

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

Vereinfache

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

Beliebte Beispiele

derivative of sqrt(4x+5)

\frac{d}{d x} (4 x + 5)

integral of sin^3(4x)cos^{-2}(4x)

\int sin^{3} (4 x) cos^{- 2} (4 x) d x

integral of cot^7(x/2)csc^2(x/2)

\int cot^{7} (\frac{x}{2}) csc^{2} (\frac{x}{2}) d x

steigung (-2,-9),(0,-3)

s l o p e (- 2, - 9), (0, - 3)

derivative of (x-3^3)

\frac{d}{d x} ((x - 3)^{3})