用对数求导数 Y=(X+1)^2*(3-X)^(1/2)*(X^2+1)^(-3)

Y=(X+1)^2*(3-X)^(1/2)*(X^2+1)^(-3),等式两边取对数,得到lny=2ln(x+1) +0。5ln(3-x) -3ln(x^2+1),等式两边对x求导,得到y'/y=2/(x+1) +1/(6-2x) - 6x/(x^2+1)= (9x^3 -11x^2- 39x+13) / [(x+1)(6-2x)(x^2+1)],等式两边乘以Y=(x+1)^2*(3-x)^(1/2)*(x^2+1)^(-3),即y'= (9x^3 -11x^2- 39x+13)/2 * (x+1) *(3-x)^(-1/2)*(x^2+1)^(-4)