d/(d{x)}({x}^2+2{y}^2+{z}^2-6{x}+3{y}-2{z}+5)

解

\frac{d}{d x} (x^{2} + 2 y^{2} + z^{2} - 6 x + 3 y - 2 z + 5)

2 x - 6

解答ステップ

\frac{d}{d x} (x^{2} + 2 y^{2} + z^{2} - 6 x + 3 y - 2 z + 5)

和/差の法則を適用:

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

= \frac{d}{d x} (x^{2}) + \frac{d}{d x} (2 y^{2}) + \frac{d}{d x} (z^{2}) - \frac{d}{d x} (6 x) + \frac{d}{d x} (3 y) - \frac{d}{d x} (2 z) + \frac{d}{d x} (5)

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

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

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

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

\frac{d}{d x} (3 y) = 0

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

\frac{d}{d x} (5) = 0

= 2 x + 0 + 0 - 6 + 0 - 0 + 0

簡素化

= 2 x - 6