derivative 5arcsin((x-1)/(x+1))

解

導関数

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

\frac{5 ( x + 1 ) ^{2}}{x ( x + 1 ) ^{2}}

解答ステップ

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

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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