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

解

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

\frac{6}{y ^{3}} + 2

解答ステップ

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

x

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

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

\frac{\partial}{\partial y} (\frac{3}{y ^{2}}) = - \frac{6}{y ^{3}}

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

= 2 - (- \frac{6}{y ^{3}}) + 0

簡素化

= \frac{6}{y ^{3}} + 2