(\partial)/(\partial x)(arcsin(l/x))

解

\frac{\partial}{\partial x} (arcsin (\frac{l}{x}))

- \frac{l}{x x ^{2} - l ^{2}}

解答ステップ

\frac{\partial}{\partial x} (arcsin (\frac{l}{x}))

連鎖法則を適用:

\frac{1}{1 - ( \frac{l}{x} ) ^{2}} \frac{\partial}{\partial x} (\frac{l}{x})

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

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

= \frac{1}{1 - ( \frac{l}{x} ) ^{2}} (- \frac{l}{x ^{2}})

簡素化

\frac{1}{1 - ( \frac{l}{x} ) ^{2}} (- \frac{l}{x ^{2}}) : - \frac{l}{x x ^{2} - l ^{2}}

= - \frac{l}{x x ^{2} - l ^{2}}