(\partial)/(\partial y)(ln(10x^2-7y^2))

解

\frac{\partial}{\partial y} (ln (10 x^{2} - 7 y^{2}))

- \frac{14 y}{10 x ^{2} - 7 y ^{2}}

解答ステップ

\frac{\partial}{\partial y} (ln (10 x^{2} - 7 y^{2}))

x

を定数として扱う

連鎖法則を適用:

\frac{1}{10 x ^{2} - 7 y ^{2}} \frac{\partial}{\partial y} (10 x^{2} - 7 y^{2})

= \frac{1}{10 x ^{2} - 7 y ^{2}} \frac{\partial}{\partial y} (10 x^{2} - 7 y^{2})

\frac{\partial}{\partial y} (10 x^{2} - 7 y^{2}) = - 14 y

= \frac{1}{10 x ^{2} - 7 y ^{2}} (- 14 y)

簡素化

\frac{1}{10 x ^{2} - 7 y ^{2}} (- 14 y) : - \frac{14 y}{10 x ^{2} - 7 y ^{2}}

= - \frac{14 y}{10 x ^{2} - 7 y ^{2}}