(\partial)/(\partial x)(ysqrt(x)-y^2-x+3y)

解

\frac{\partial}{\partial x} (y x - y^{2} - x + 3 y)

\frac{y}{2 x} - 1

解答ステップ

\frac{\partial}{\partial x} (y x - y^{2} - x + 3 y)

y

を定数として扱う

和/差の法則を適用:

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

= \frac{\partial}{\partial x} (y x) - \frac{\partial}{\partial x} (y^{2}) - \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (3 y)

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

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

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

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

= \frac{y}{2 x} - 0 - 1 + 0

簡素化

= \frac{y}{2 x} - 1