derivative (arcsin(5x+5))^8

解

導関数

(arcsin (5 x + 5))^{8}

\frac{40 arcsin ^{7} ( 5 x + 5 )}{- 25 x ^{2} - 50 x - 24}

解答ステップ

\frac{d}{d x} ((arcsin (5 x + 5))^{8})

連鎖法則を適用:

8 (arcsin (5 x + 5))^{7} \frac{d}{d x} (arcsin (5 x + 5))

= 8 (arcsin (5 x + 5))^{7} \frac{d}{d x} (arcsin (5 x + 5))

\frac{d}{d x} (arcsin (5 x + 5)) = \frac{5}{- 25 x ^{2} - 50 x - 24}

= 8 (arcsin (5 x + 5))^{7} \frac{5}{- 25 x ^{2} - 50 x - 24}

簡素化

8 arcsin^{7} (5 x + 5) \frac{5}{- 25 x ^{2} - 50 x - 24} : \frac{40 arcsin ^{7} ( 5 x + 5 )}{- 25 x ^{2} - 50 x - 24}

= \frac{40 arcsin ^{7} ( 5 x + 5 )}{- 25 x ^{2} - 50 x - 24}