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Beliebt Rechnen >

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

Lösung

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

Lösung

x^{2} - 2 y - 4

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

\frac{\partial}{\partial y} (4 y) = 4

= 0 + x^{2} - 2 y - 4

Vereinfache

= x^{2} - 2 y - 4

Beliebte Beispiele

integral from-1 to 2 of (x-1)(2x+3)

\int_{- 1}^{2} (x - 1) (2 x + 3) d x

derivative of-64e^{-4x}

\frac{d}{d x} (- 64 e^{- 4 x})

integral of ycos(x)y

\int y cos (x) y d x

limit as x approaches 0 of (1-1/(x+1))/x

x \to 0 lim (\frac{1 - \frac{1}{x + 1}}{x})

steigung (0,0),(5,4)

s l o p e (0, 0), (5, 4)