(\partial)/(\partial x)(arcsin(xy))

解

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

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

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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

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