<\/p>\n
\u9006\u4e09\u89d2\u95a2\u6570 \\(y = \\sin^{-1} x\\) \u306f \u4e09\u89d2\u95a2\u6570 \\(x = \\sin y\\) \u306e\u9006\u95a2\u6570\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u305d\u306e\u5fae\u5206\u306f\uff08\u5b66\u90e81\u5e74\u751f\u3067\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u6559\u3048\u308b\uff09
\n\\begin{eqnarray}
\n\\frac{d}{dx} \\sin^{-1} x &=& \\frac{dy}{dx} \\\\
\n&=& \\frac{1}{\\frac{dx}{dy}} \\\\
\n&=& \\frac{1}{\\cos y} \\\\
\n&=& \\frac{1}{\\sqrt{1 – \\sin^2 y}}\\\\
\n&=& \\frac{1}{\\sqrt{1-x^2}}\\\\
\n\\therefore\\ \\ \\frac{d}{dx} \\sin^{-1} x &=&\\frac{1}{\\sqrt{1-x^2}}
\n\\end{eqnarray}
\n\u540c\u69d8\u306b\u3057\u3066\uff0c\u4ee5\u4e0b\u3082\u308f\u304b\u308b\u3002
\n\\begin{eqnarray}
\n\\frac{d}{dx} \\cos^{-1} x &=& – \\frac{1}{\\sqrt{1-x^2}}
\n\\end{eqnarray}<\/p>\n
\u4e0a\u8a18\u306e\u5fae\u5206\u7d50\u679c\u304b\u3089\uff0c\u5927\u5b661\u5e74\u3067\u7fd2\u3046\u7a4d\u5206\u516c\u5f0f\uff08\u7d50\u679c\u304c\u9006\u4e09\u89d2\u95a2\u6570\u3067\u66f8\u3051\u308b\u3084\u3064\uff09\u306f
$$ \\int\\frac{dx}{\\sqrt{1-x^2}} = \\sin^{-1} x, \\quad -\\int\\frac{dx}{\\sqrt{1-x^2}} = \\cos^{-1} x$$<\/p>\n
\u3068\u6559\u308f\u3063\u305f\u304b\u3082\u3057\u308c\u306a\u3044\u3002\u3067\u3082\u3053\u308c\u3060\u3068\uff0c\u540c\u3058\u7a4d\u5206 \\(\\displaystyle \\int\\frac{dx}{\\sqrt{1-x^2}}\\) \u306e\u7b54\u3048\u304c \\(\\sin^{-1} x\\) \u3067\u3082\u3044\u3044\u3057\uff0c\\( -\\cos^{-1} x\\) \u3067\u3082\u3044\u3044\u3053\u3068\u306b\u306a\u308a\uff0c\u4e00\u610f\u306b\u6c7a\u307e\u3089\u306a\u3044\u3088\u3046\u306b\u601d\u3048\u308b\u304c\uff0c\u305d\u306e\u8fba\u306f\u7a4d\u5206\u5b9a\u6570\u3067\u5438\u53ce\u3067\u304d\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u304a\u3053\u3046\u3002<\/p>\n