derivative f(x)=arcsin(6x+1)

解

derivative

\frac{6}{- 36 x ^{2} - 12 x}

解答ステップ

\frac{d}{d x} (arcsin (6 x + 1))

連鎖法則を適用:

\frac{1}{1 - ( 6 x + 1 ) ^{2}} \frac{d}{d x} (6 x + 1)

= \frac{1}{1 - ( 6 x + 1 ) ^{2}} \frac{d}{d x} (6 x + 1)

\frac{d}{d x} (6 x + 1) = 6

= \frac{1}{1 - ( 6 x + 1 ) ^{2}} \cdot 6

簡素化

\frac{1}{1 - ( 6 x + 1 ) ^{2}} \cdot 6 : \frac{6}{- 36 x ^{2} - 12 x}

= \frac{6}{- 36 x ^{2} - 12 x}