{"id":98,"date":"2026-10-14T12:13:34","date_gmt":"2026-10-14T12:13:34","guid":{"rendered":"https:\/\/mudhakara.com\/?p=98"},"modified":"2026-11-05T09:24:25","modified_gmt":"2026-11-05T09:24:25","slug":"derivatives-in-three-days","status":"publish","type":"post","link":"https:\/\/mudhakara.com\/?p=98","title":{"rendered":"\u0643\u064a\u0641 \u062a\u0631\u0627\u062c\u0639 \u0648\u062d\u062f\u0629 \u0627\u0644\u062a\u0641\u0627\u0636\u0644 \u0641\u064a \u062b\u0644\u0627\u062b\u0629 \u0623\u064a\u0627\u0645"},"content":{"rendered":"

\u0625\u0630\u0627 \u0643\u0627\u0646 \u0623\u0645\u0627\u0645\u0643 \u062b\u0644\u0627\u062b\u0629 \u0623\u064a\u0627\u0645 \u0641\u0642\u0637 \u0642\u0628\u0644 \u0627\u062e\u062a\u0628\u0627\u0631 \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u060c \u0641\u0644\u0627 \u062a\u062d\u0627\u0648\u0644 \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0648\u062d\u062f\u0629 \u0643\u0644\u0647\u0627 \u0645\u0631\u0629 \u0648\u0627\u062d\u062f\u0629. \u062b\u0644\u0627\u062b\u0629 \u0623\u064a\u0627\u0645 \u062a\u0643\u0641\u064a \u0625\u0646 \u0642\u0633\u0645\u062a\u0647\u0627 \u0628\u0630\u0643\u0627\u0621: \u064a\u0648\u0645 \u0644\u0644\u0642\u0648\u0627\u0639\u062f\u060c \u0648\u064a\u0648\u0645 \u0644\u0644\u0623\u0633\u0626\u0644\u0629\u060c \u0648\u064a\u0648\u0645 \u0644\u0623\u062e\u0637\u0627\u0626\u0643. \u0647\u0630\u0647 \u0627\u0644\u062e\u0637\u0629 \u062a\u0641\u062a\u0631\u0636 \u0623\u0646\u0643 \u062f\u0631\u0633\u062a \u0627\u0644\u0648\u062d\u062f\u0629 \u0641\u064a \u0627\u0644\u0635\u0641 \u0645\u0646 \u0642\u0628\u0644\u060c \u0648\u062a\u0631\u064a\u062f \u062a\u062b\u0628\u064a\u062a\u0647\u0627 \u0644\u0627 \u062a\u0639\u0644\u0651\u0645\u0647\u0627 \u0645\u0646 \u0627\u0644\u0635\u0641\u0631.<\/p>\n

\u0627\u0644\u064a\u0648\u0645 \u0627\u0644\u0623\u0648\u0644: \u0627\u0644\u0642\u0648\u0627\u0639\u062f \u0628\u064a\u062f\u0643<\/h2>\n

\u0627\u0628\u062f\u0623 \u0628\u0648\u0631\u0642\u0629 \u0628\u064a\u0636\u0627\u0621\u060c \u0648\u0627\u0643\u062a\u0628 \u0643\u0644 \u0642\u0627\u0639\u062f\u0629 \u0627\u0634\u062a\u0642\u0627\u0642 \u062a\u0639\u0631\u0641\u0647\u0627 \u062f\u0648\u0646 \u0627\u0644\u0646\u0638\u0631 \u0625\u0644\u0649 \u0627\u0644\u0643\u062a\u0627\u0628. \u0628\u0639\u062f \u0639\u0634\u0631 \u062f\u0642\u0627\u0626\u0642 \u0627\u0641\u062a\u062d \u0627\u0644\u0643\u062a\u0627\u0628 \u0648\u0642\u0627\u0631\u0646. \u0645\u0627 \u0646\u0633\u064a\u062a\u0647 \u0647\u0648 \u0645\u0627 \u062a\u062d\u062a\u0627\u062c \u0645\u0631\u0627\u062c\u0639\u062a\u0647 \u0641\u0639\u0644\u064b\u0627\u060c \u0648\u0645\u0627 \u0643\u062a\u0628\u062a\u0647 \u0635\u062d\u064a\u062d\u064b\u0627 \u0644\u0627 \u064a\u062d\u062a\u0627\u062c \u0648\u0642\u062a\u064b\u0627 \u0625\u0636\u0627\u0641\u064a\u064b\u0627.<\/p>\n

\u0627\u0644\u0642\u0648\u0627\u0639\u062f \u0627\u0644\u062a\u064a \u0644\u0627 \u063a\u0646\u0649 \u0639\u0646\u0647\u0627<\/h3>\n
\n\n\n\n\n\n\n\n\n\n
\u0627\u0644\u0642\u0627\u0639\u062f\u0629<\/th>\n\u0627\u0644\u0635\u064a\u063a\u0629<\/th>\n\u0645\u062b\u0627\u0644<\/th>\n<\/tr>\n<\/thead>\n
\u0627\u0644\u0642\u0648\u0629<\/td>\n(x\u207f)\u2032 = n\u00b7x\u207f\u207b\u00b9<\/bdi><\/td>\n(x\u00b3)\u2032 = 3x\u00b2<\/bdi><\/td>\n<\/tr>\n
\u0627\u0644\u062b\u0627\u0628\u062a<\/td>\n(c)\u2032 = 0<\/bdi><\/td>\n(7)\u2032 = 0<\/bdi><\/td>\n<\/tr>\n
\u0627\u0644\u0636\u0631\u0628<\/td>\n(u\u00b7v)\u2032 = u\u2032v + uv\u2032<\/bdi><\/td>\n(x\u00b7sin x)\u2032 = sin x + x\u00b7cos x<\/bdi><\/td>\n<\/tr>\n
\u0627\u0644\u0642\u0633\u0645\u0629<\/td>\n(u\/v)\u2032 = (u\u2032v \u2212 uv\u2032)\/v\u00b2<\/bdi><\/td>\n(1\/x)\u2032 = \u22121\/x\u00b2<\/bdi><\/td>\n<\/tr>\n
\u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629<\/td>\n(sin x)\u2032 = cos x<\/bdi><\/td>\n(cos x)\u2032 = \u2212sin x<\/bdi><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/figure>\n

\u0627\u0643\u062a\u0628 \u0643\u0644 \u0642\u0627\u0639\u062f\u0629 \u062b\u0644\u0627\u062b \u0645\u0631\u0627\u062a \u0645\u0639 \u0645\u062b\u0627\u0644 \u0645\u0646 \u0639\u0646\u062f\u0643. \u0627\u0644\u0643\u062a\u0627\u0628\u0629 \u0628\u0627\u0644\u064a\u062f \u062a\u062b\u0628\u062a \u0627\u0644\u0635\u064a\u063a\u0629 \u0623\u0643\u062b\u0631 \u0645\u0646 \u0627\u0644\u0642\u0631\u0627\u0621\u0629.<\/p>\n

\u0646\u0635\u064a\u062d\u0629<\/strong><\/p>\n

\u0644\u0627 \u062a\u0646\u062a\u0642\u0644 \u0625\u0644\u0649 \u0627\u0644\u064a\u0648\u0645 \u0627\u0644\u062b\u0627\u0646\u064a \u0642\u0628\u0644 \u0623\u0646 \u062a\u0643\u062a\u0628 \u0627\u0644\u0642\u0648\u0627\u0639\u062f \u0627\u0644\u062e\u0645\u0633 \u0643\u0644\u0647\u0627 \u0645\u0646 \u0627\u0644\u0630\u0627\u0643\u0631\u0629 \u062f\u0648\u0646 \u062e\u0637\u0623.<\/p>\n<\/div>\n

\u0627\u0644\u064a\u0648\u0645 \u0627\u0644\u062b\u0627\u0646\u064a: \u0627\u0644\u0623\u0633\u0626\u0644\u0629 \u0628\u0627\u0644\u062a\u062f\u0631\u064a\u062c<\/h2>\n

\u0627\u0644\u064a\u0648\u0645 \u0644\u0644\u062a\u0637\u0628\u064a\u0642. \u0627\u0628\u062f\u0623 \u0628\u0627\u0644\u0623\u0633\u0626\u0644\u0629 \u0627\u0644\u0633\u0647\u0644\u0629 \u062b\u0645 \u0627\u0644\u0645\u062a\u0648\u0633\u0637\u0629 \u062b\u0645 \u0627\u0644\u0635\u0639\u0628\u0629\u060c \u0648\u0644\u0627 \u062a\u0642\u0641\u0632 \u0645\u0628\u0627\u0634\u0631\u0629 \u0625\u0644\u0649 \u0627\u0644\u0635\u0639\u0628 \u0644\u0623\u0646\u0647 \u064a\u0633\u062a\u0647\u0644\u0643 \u0648\u0642\u062a\u0643 \u0648\u064a\u0647\u0632 \u062b\u0642\u062a\u0643.<\/p>\n

\u0643\u064a\u0641 \u062a\u062d\u0644 \u0643\u0644 \u0633\u0624\u0627\u0644<\/h3>\n
    \n
  1. \u0627\u0642\u0631\u0623 \u0627\u0644\u062f\u0627\u0644\u0629 \u0648\u062d\u062f\u062f \u0646\u0648\u0639\u0647\u0627: \u0642\u0648\u0629\u060c \u0636\u0631\u0628\u060c \u0642\u0633\u0645\u0629\u060c \u0623\u0645 \u0645\u0631\u0643\u0651\u0628\u0629.<\/li>\n
  2. \u0627\u062e\u062a\u0631 \u0627\u0644\u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0645\u0646\u0627\u0633\u0628\u0629 \u0648\u0627\u0643\u062a\u0628\u0647\u0627 \u0641\u0648\u0642 \u0627\u0644\u0633\u0624\u0627\u0644.<\/li>\n
  3. \u0646\u0641\u0651\u0630 \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0648\u0627\u062d\u062f\u0629 \u0648\u0627\u062d\u062f\u0629\u060c \u0648\u0644\u0627 \u062a\u062e\u062a\u0635\u0631 \u0641\u064a \u0627\u0644\u0630\u0647\u0646.<\/li>\n
  4. \u0627\u0642\u0631\u0623 \u0627\u0644\u0634\u0631\u062d \u0628\u0639\u062f \u0643\u0644 \u0633\u0624\u0627\u0644\u060c \u062d\u062a\u0649 \u0644\u0648 \u0643\u0627\u0646\u062a \u0625\u062c\u0627\u0628\u062a\u0643 \u0635\u062d\u064a\u062d\u0629.<\/li>\n<\/ol>\n

    \u0642\u0631\u0627\u0621\u0629 \u0627\u0644\u0634\u0631\u062d \u0628\u0639\u062f \u0627\u0644\u0625\u062c\u0627\u0628\u0629 \u0627\u0644\u0635\u062d\u064a\u062d\u0629 \u0644\u064a\u0633\u062a \u0645\u0636\u064a\u0639\u0629 \u0644\u0644\u0648\u0642\u062a. \u0623\u062d\u064a\u0627\u0646\u064b\u0627 \u062a\u0635\u0644 \u0625\u0644\u0649 \u0627\u0644\u062c\u0648\u0627\u0628 \u0627\u0644\u0635\u062d\u064a\u062d \u0628\u0637\u0631\u064a\u0642\u0629 \u062e\u0627\u0637\u0626\u0629\u060c \u0648\u0627\u0644\u0634\u0631\u062d \u064a\u0643\u0634\u0641 \u0630\u0644\u0643 \u0642\u0628\u0644 \u0627\u0644\u0627\u0645\u062a\u062d\u0627\u0646.<\/p>\n

    \u0645\u064a\u0644 \u0627\u0644\u0645\u0645\u0627\u0633: \u0627\u0644\u0633\u0624\u0627\u0644 \u0627\u0644\u0623\u0643\u062b\u0631 \u062a\u0643\u0631\u0627\u0631\u064b\u0627<\/h3>\n

    \u0643\u062b\u064a\u0631 \u0645\u0646 \u0623\u0633\u0626\u0644\u0629 \u0627\u0644\u062a\u0641\u0627\u0636\u0644 \u062a\u0637\u0644\u0628 \u0645\u064a\u0644 \u0627\u0644\u0645\u0645\u0627\u0633 \u0639\u0646\u062f \u0646\u0642\u0637\u0629. \u0627\u0644\u0641\u0643\u0631\u0629 \u0628\u0633\u064a\u0637\u0629: \u0627\u0644\u0645\u064a\u0644 \u064a\u0633\u0627\u0648\u064a \u0642\u064a\u0645\u0629 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0639\u0646\u062f \u062a\u0644\u0643 \u0627\u0644\u0646\u0642\u0637\u0629. \u0627\u0634\u062a\u0642 \u0627\u0644\u062f\u0627\u0644\u0629 \u0623\u0648\u0644\u064b\u0627\u060c \u062b\u0645 \u0639\u0648\u0651\u0636 \u0628\u0642\u064a\u0645\u0629 x. \u0645\u062b\u0644\u064b\u0627\u060c \u0645\u064a\u0644 \u0627\u0644\u0645\u0645\u0627\u0633 \u0644\u0645\u0646\u062d\u0646\u0649 f(x) = x\u00b2<\/bdi> \u0639\u0646\u062f x = 3<\/bdi> \u0647\u0648 f\u2032(3) = 2 \u00d7 3 = 6<\/bdi>.<\/p>\n

    \u0627\u0644\u064a\u0648\u0645 \u0627\u0644\u062b\u0627\u0644\u062b: \u0623\u062e\u0637\u0627\u0624\u0643 \u0641\u0642\u0637<\/h2>\n

    \u0644\u0627 \u062a\u062d\u0644 \u0623\u0633\u0626\u0644\u0629 \u062c\u062f\u064a\u062f\u0629 \u0641\u064a \u0627\u0644\u064a\u0648\u0645 \u0627\u0644\u0623\u062e\u064a\u0631. \u0623\u0639\u062f \u0627\u0644\u0623\u0633\u0626\u0644\u0629 \u0627\u0644\u062a\u064a \u0623\u062e\u0637\u0623\u062a \u0641\u064a\u0647\u0627 \u0623\u0645\u0633\u060c \u062f\u0648\u0646 \u0627\u0644\u0646\u0638\u0631 \u0625\u0644\u0649 \u0627\u0644\u062d\u0644. \u0647\u0630\u0647 \u0627\u0644\u0623\u0633\u0626\u0644\u0629 \u062a\u0645\u062b\u0644 \u0646\u0642\u0627\u0637 \u0636\u0639\u0641\u0643 \u0627\u0644\u062d\u0642\u064a\u0642\u064a\u0629\u060c \u0648\u0645\u0639\u0627\u0644\u062c\u062a\u0647\u0627 \u0623\u0646\u0641\u0639 \u0645\u0646 \u0639\u0634\u0631\u064a\u0646 \u0633\u0624\u0627\u0644\u064b\u0627 \u062c\u062f\u064a\u062f\u064b\u0627.<\/p>\n

    \u0625\u0630\u0627 \u0623\u062e\u0637\u0623\u062a \u0641\u064a \u0627\u0644\u0633\u0624\u0627\u0644 \u0646\u0641\u0633\u0647 \u0645\u0631\u062a\u064a\u0646\u060c \u0641\u0627\u0643\u062a\u0628 \u0627\u0644\u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0645\u0631\u062a\u0628\u0637\u0629 \u0628\u0647 \u0639\u0644\u0649 \u0628\u0637\u0627\u0642\u0629 \u0635\u063a\u064a\u0631\u0629\u060c \u0648\u0631\u0627\u062c\u0639\u0647\u0627 \u0635\u0628\u0627\u062d \u064a\u0648\u0645 \u0627\u0644\u0627\u062e\u062a\u0628\u0627\u0631. \u0628\u0637\u0627\u0642\u0629 \u0648\u0627\u062d\u062f\u0629 \u0644\u0643\u0644 \u062e\u0637\u0623 \u0645\u062a\u0643\u0631\u0631 \u062a\u0643\u0641\u064a.<\/p>\n

    \u0639\u0644\u0627\u0645\u0627\u062a \u0623\u0646\u0643 \u062c\u0627\u0647\u0632<\/h3>\n
      \n
    • \u062a\u0643\u062a\u0628 \u0627\u0644\u0642\u0648\u0627\u0639\u062f \u0627\u0644\u062e\u0645\u0633 \u0645\u0646 \u0627\u0644\u0630\u0627\u0643\u0631\u0629.<\/li>\n
    • \u062a\u062d\u0644 \u0633\u0624\u0627\u0644\u064b\u0627 \u0645\u062a\u0648\u0633\u0637\u064b\u0627 \u0641\u064a \u0623\u0642\u0644 \u0645\u0646 \u062b\u0644\u0627\u062b \u062f\u0642\u0627\u0626\u0642.<\/li>\n
    • \u062a\u0639\u0631\u0641 \u0645\u062a\u0649 \u062a\u0633\u062a\u062e\u062f\u0645 \u0642\u0627\u0639\u062f\u0629 \u0627\u0644\u0636\u0631\u0628 \u0648\u0645\u062a\u0649 \u062a\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0642\u0633\u0645\u0629.<\/li>\n
    • \u0623\u062e\u0637\u0627\u0624\u0643 \u0641\u064a \u0627\u0644\u064a\u0648\u0645 \u0627\u0644\u062b\u0627\u0644\u062b \u0623\u0642\u0644 \u0645\u0646 \u0646\u0635\u0641 \u0623\u062e\u0637\u0627\u0626\u0643 \u0641\u064a \u0627\u0644\u064a\u0648\u0645 \u0627\u0644\u062b\u0627\u0646\u064a.<\/li>\n<\/ul>\n

      \u0628\u0639\u062f \u0627\u0644\u0627\u062e\u062a\u0628\u0627\u0631<\/h2>\n

      \u0644\u0627 \u062a\u062d\u0630\u0641 \u0628\u0637\u0627\u0642\u0627\u062a \u0627\u0644\u0623\u062e\u0637\u0627\u0621. \u0627\u0644\u062a\u0641\u0627\u0636\u0644 \u0623\u0633\u0627\u0633 \u0648\u062d\u062f\u0629 \u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0627\u0644\u062a\u064a \u062a\u0644\u064a\u0647\u060c \u0648\u0633\u062a\u062d\u062a\u0627\u062c \u0627\u0644\u0642\u0648\u0627\u0639\u062f \u0646\u0641\u0633\u0647\u0627 \u062d\u064a\u0646 \u062a\u0628\u062f\u0623 \u0628\u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0639\u0643\u0633\u064a\u064b\u0627. \u0627\u062d\u062a\u0641\u0638 \u0628\u0627\u0644\u0628\u0637\u0627\u0642\u0627\u062a\u060c \u0648\u0631\u0627\u062c\u0639\u0647\u0627 \u0628\u0639\u062f \u0623\u0633\u0628\u0648\u0639 \u0645\u0631\u0629 \u0648\u0627\u062d\u062f\u0629 \u0644\u062a\u0628\u0642\u0649 \u0627\u0644\u0642\u0648\u0627\u0639\u062f \u062d\u0627\u0636\u0631\u0629.<\/p>\n

      \u0623\u0633\u0626\u0644\u0629 \u064a\u0637\u0631\u062d\u0647\u0627 \u0627\u0644\u0637\u0644\u0627\u0628 \u0639\u0646 \u0647\u0630\u0647 \u0627\u0644\u062e\u0637\u0629<\/h2>\n

      \u0647\u0644 \u062a\u0643\u0641\u064a \u062b\u0644\u0627\u062b\u0629 \u0623\u064a\u0627\u0645 \u0641\u0639\u0644\u064b\u0627\u061f<\/h3>\n

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