d/(d{x)}(({z}(x,y))({x}^2+2{y}^2-6{x}-8{y}+20))

Lösung

\frac{d}{d x} ((z (x, y)) (x^{2} + 2 y^{2} - 6 x - 8 y + 20))

z (x, y) (2 x + 0 - 6 - 0 + 0)

Schritte zur Lösung

\frac{d}{d x} ((z (x, y)) (x^{2} + 2 y^{2} - 6 x - 8 y + 20))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= z (x, y) \frac{d}{d x} (x^{2} + 2 y^{2} - 6 x - 8 y + 20)

Wende die Summen-/Differenzregel an:

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

= z (x, y) (\frac{d}{d x} (x^{2}) + \frac{d}{d x} (2 y^{2}) - \frac{d}{d x} (6 x) - \frac{d}{d x} (8 y) + \frac{d}{d x} (20))

\frac{d}{d x} (x^{2}) = 2 x

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

\frac{d}{d x} (6 x) = 6

\frac{d}{d x} (8 y) = 0

\frac{d}{d x} (20) = 0

= z (x, y) (2 x + 0 - 6 - 0 + 0)

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