(\partial)/(\partial x)(x(1-x-2y))

Lösung

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

- 2 x - 2 y + 1

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x, g = 1 - x - 2 y

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

\frac{\partial}{\partial x} (x) = 1

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

= 1 \cdot (1 - x - 2 y) + (- 1) x

Vereinfache

1 \cdot (1 - x - 2 y) + (- 1) x : - 2 x - 2 y + 1

= - 2 x - 2 y + 1

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

d er i v a t i v e π^{2}

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a re a 5 - x^{2}, 2 - 2 x

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