derivative y=arcsin(x+1)

解

derivative

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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