Question

用对数求导法求函数的导数

用对数求导法求下列函数的导数请给出步骤和答案,拜谢

Answer 1

lny=1/2ln(x+2)+4ln(3-x)-5ln(x+1)两边求导 1/y*y'=1/2x+4-4/3-x+5/x+1所以y‘=y[1/2x+4-4/3-x+5/x+1]

Answer 2

因为y=[√(x+2)(3-x)^4]/(x+1)^5所以lny=ln[√(x+2)]+ln(3-x)^4-ln(x+1)^5所以lny=(1/2)ln[(x+2)]+4ln(3-x)-5ln(x+1)所以(1/y)y'=(1/2)(1/x+2)+4×(-1)(1/3-x)-5/(x+1)(1/y)y'=(1/2x+4)+4(x-3)-5/(x+1)(1/y)y'=(1/2x+4)+4x-12-5/(x+1)因为y=[√(x+2)(3-x)^4]/(x+1)^5所以y'=y[(1/2x+4)+4x-12-5/(x+1)]=[√(x+2)(3-x)^4]/(x+1)^5][(1/2x+4)+4x-12-5/(x+1)]

Answer 3