(\partial)/(\partial x)(xzsqrt(x+y))

解

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

\frac{z ( 3 x + 2 y )}{2 x + y}

解答ステップ

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

z, y

を定数として扱う

定数を除去:

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

= z \frac{\partial}{\partial x} (x x + y)

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x + y

= z (\frac{\partial}{\partial x} (x) x + y + \frac{\partial}{\partial x} (x + y) x)

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

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

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

簡素化

z (1 \cdot x + y + \frac{1}{2 x + y} x) : \frac{z ( 3 x + 2 y )}{2 x + y}

= \frac{z ( 3 x + 2 y )}{2 x + y}