(\partial)/(\partial x)(-y/(x^2)+4x+1/y)

解

\frac{\partial}{\partial x} (- \frac{y}{x ^{2}} + 4 x + \frac{1}{y})

\frac{2 y}{x ^{3}} + 4

解答ステップ

\frac{\partial}{\partial x} (- \frac{y}{x ^{2}} + 4 x + \frac{1}{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} (\frac{y}{x ^{2}}) + \frac{\partial}{\partial x} (4 x) + \frac{\partial}{\partial x} (\frac{1}{y})

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

\frac{\partial}{\partial x} (4 x) = 4

\frac{\partial}{\partial x} (\frac{1}{y}) = 0

= - (- \frac{2 y}{x ^{3}}) + 4 + 0

簡素化

= \frac{2 y}{x ^{3}} + 4