用对数求导法求导数：5次根号下【（x-5）/5次根号下（x^2+2）】

y= ( (x-5)/(x^2+2)^(1/5) )^(1/5)两边同时求导lny= ln( (x-5)/(x^2+2)^(1/5) )^(1/5)lny= 1/5*ln((x-5)/(x^2+2)^(1/5))lny= 1/5*( ln(x-5)- 1/5*ln(x^2+2) )两边同时求导y'/y= 1/5*( 1/(x-5) - 1/5* 2x/(x^2+2) )y'/y= (3x^2+10x+10)/(25(x-5)(x^2+2))y'=y*(3x^2+10x+10)/(25(x-5)(x^2+2))y'=(3x^2+10x+10)/(25(x-5)(x^2+2))*( (x-5)/(x^2+2)^(1/5) )^(1/5)函数y=x^5+x 函数连续导数y'=5x^4+1>0所以函数单调递增x=0 y=0所以只能有一个x>0 满足x^5+x-1=0。