(\partial)/(\partial x)(arcsin(5x))

解

\frac{\partial}{\partial x} (arcsin (5 x))

\frac{5}{1 - 25 x ^{2}}

解答ステップ

\frac{\partial}{\partial x} (arcsin (5 x))

連鎖法則を適用:

\frac{1}{1 - ( 5 x ) ^{2}} \frac{\partial}{\partial x} (5 x)

= \frac{1}{1 - ( 5 x ) ^{2}} \frac{\partial}{\partial x} (5 x)

\frac{\partial}{\partial x} (5 x) = 5

= \frac{1}{1 - ( 5 x ) ^{2}} \cdot 5

簡素化

\frac{1}{1 - ( 5 x ) ^{2}} \cdot 5 : \frac{5}{1 - 25 x ^{2}}

= \frac{5}{1 - 25 x ^{2}}