(\partial)/(\partial x)((x^2-2y)(y^2-x))

Lösung

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

2 x y^{2} - 3 x^{2} + 2 y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2} - 2 y, g = y^{2} - x

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

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

\frac{\partial}{\partial x} (y^{2} - x) = - 1

= 2 x (y^{2} - x) + (- 1) (x^{2} - 2 y)

Vereinfache

2 x (y^{2} - x) + (- 1) (x^{2} - 2 y) : 2 x y^{2} - 3 x^{2} + 2 y

= 2 x y^{2} - 3 x^{2} + 2 y

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