d/(d{x)}(4{x}-3{x}^2-{y}^2-({z}-1)^2)

Lösung

\frac{d}{d x} (4 x - 3 x^{2} - y^{2} - (z - 1)^{2})

- 6 x + 4

Schritte zur Lösung

\frac{d}{d x} (4 x - 3 x^{2} - y^{2} - (z - 1)^{2})

Vereinfache

4 x - 3 x^{2} - y^{2} - (z - 1)^{2} : 4 x - 3 x^{2} - y^{2} - z^{2} + 2 z - 1

= \frac{d}{d x} (4 x - 3 x^{2} - y^{2} - z^{2} + 2 z - 1)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (4 x) - \frac{d}{d x} (3 x^{2}) - \frac{d}{d x} (y^{2}) - \frac{d}{d x} (z^{2}) + \frac{d}{d x} (2 z) - \frac{d}{d x} (1)

\frac{d}{d x} (4 x) = 4

\frac{d}{d x} (3 x^{2}) = 6 x

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

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

\frac{d}{d x} (2 z) = 0

\frac{d}{d x} (1) = 0

= 4 - 6 x - 0 - 0 + 0 - 0

Vereinfache

= - 6 x + 4