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

解

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

\frac{1 + \frac{d}{d x} ( y ) + \frac{d}{d x} ( z )}{2 x + y + z}

解答ステップ

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

連鎖法則を適用:

\frac{1}{2 x + y + z} \frac{d}{d x} (x + y + z)

= \frac{1}{2 x + y + z} \frac{d}{d x} (x + y + z)

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

= \frac{1}{2 x + y + z} (1 + \frac{d}{d x} (y) + \frac{d}{d x} (z))

= \frac{1}{2 x + y + z} (1 + \frac{d}{d x} (y) + \frac{d}{d x} (z))

簡素化

\frac{1}{2 x + y + z} (1 + \frac{d}{d x} (y) + \frac{d}{d x} (z)) : \frac{1 + \frac{d}{d x} ( y ) + \frac{d}{d x} ( z )}{2 x + y + z}

= \frac{1 + \frac{d}{d x} ( y ) + \frac{d}{d x} ( z )}{2 x + y + z}