è¿ä¸ªæ¯éå½æ°çé®é¢,å°±æ¯è¯´æ²¡æåæï¼ææ¾çyåxä¹é´çå
³ç³»å¼,æ¯å¦y=arctan(x).
ä½æ¯å¯ä»¥ç¨éå½æ°çæ±å¯¼æ³åï¼
â 两边åæ¶å¯¹xæ±å¯¼,(æ±å¯¼å®é
ä¸ä¹æ¯ä¸ç§è¿ç®),å¾å°ï¼
dy/dx=1/[1+(x+y)^2] * [1+dy/dx] -------------è¿éå³ç«¯å项ç[1+dy/dx] 表示d(x+y)/dxï¼
å项表示arctan对xç导æ°.
æ两边çdy/dxå并,æ以ï¼ä¸é¶å¯¼æ° dy/dx=1/(x+y)^2 â´
â¡ ä¸é¢â´å¼ä¸¤è¾¹ç»§ç»å¯¹xæ±å¯¼ï¼
d2y/dx2= -2/(x+y)^3 * (1+dy/dx)
ï¼-2/(x+y)^3 * (1+dy/dx)
ï¼-2/(x+y)^3 * (1+1/(x+y)^2)
ï¼-2[1+(x+y)^2] / (x+y)^5
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ï¼ï¼2[1+(x+y)^2] ï¼2 / (x+y)^5 âµ
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