(\partial)/(\partial y)(x^2yz+1/(xyz^2))

解

\frac{\partial}{\partial y} (x^{2} yz + \frac{1}{x y z ^{2}})

x^{2} z - \frac{1}{x z ^{2} y ^{2}}

解答ステップ

\frac{\partial}{\partial y} (x^{2} yz + \frac{1}{x y z ^{2}})

x, z

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} (x^{2} yz) + \frac{\partial}{\partial y} (\frac{1}{x y z ^{2}})

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

\frac{\partial}{\partial y} (\frac{1}{x y z ^{2}}) = - \frac{1}{x z ^{2} y ^{2}}

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