(\partial)/(\partial x)(x^{-7}y^2+xy^2+2xy)

解

\frac{\partial}{\partial x} (x^{- 7} y^{2} + x y^{2} + 2 x y)

- \frac{7 y ^{2}}{x ^{8}} + y^{2} + 2 y

解答ステップ

\frac{\partial}{\partial x} (x^{- 7} y^{2} + x y^{2} + 2 x 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} (x^{- 7} y^{2}) + \frac{\partial}{\partial x} (x y^{2}) + \frac{\partial}{\partial x} (2 x y)

\frac{\partial}{\partial x} (x^{- 7} y^{2}) = - \frac{7 y ^{2}}{x ^{8}}

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

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

= - \frac{7 y ^{2}}{x ^{8}} + y^{2} + 2 y