derivative of arcsin(5x-1)

解

\frac{d}{d x} (arcsin (5 x - 1))

\frac{5}{- 25 x ^{2} + 10 x}

解答ステップ

\frac{d}{d x} (arcsin (5 x - 1))

連鎖法則を適用:

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

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

\frac{d}{d x} (5 x - 1) = 5

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

簡素化

\frac{1}{1 - ( 5 x - 1 ) ^{2}} \cdot 5 : \frac{5}{- 25 x ^{2} + 10 x}

= \frac{5}{- 25 x ^{2} + 10 x}