d/(d{x)}(({z})({x}+2{y}+{z}-2sqrt({x){y}{z}}))

解

\frac{d}{d x} ((z) (x + 2 y + z - 2 x y z))

z (\frac{d}{d x} (z) + 1 - \frac{y z}{x})

解答ステップ

\frac{d}{d x} ((z) (x + 2 y + z - 2 x y z))

定数を除去:

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

= z \frac{d}{d x} (x + 2 y + z - 2 x y z)

和/差の法則を適用:

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

= z (\frac{d}{d x} (x) + \frac{d}{d x} (2 y) + \frac{d}{d x} (z) - \frac{d}{d x} (2 x y z))

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

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

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

= z (1 + 0 + \frac{d}{d x} (z) - \frac{y z}{x})

簡素化

= z (\frac{d}{d x} (z) + 1 - \frac{y z}{x})