求导:y=√(x^2+4x)/(x^3+2) ^1/3

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/27 05:11:52
求导:y=√(x^2+4x)/(x^3+2)^1/3求导:y=√(x^2+4x)/(x^3+2)^1/3求导:y=√(x^2+4x)/(x^3+2)^1/3对数求导法lny=(1/2)ln(x^2+4

求导:y=√(x^2+4x)/(x^3+2) ^1/3
求导:y=√(x^2+4x)/(x^3+2) ^1/3

求导:y=√(x^2+4x)/(x^3+2) ^1/3
对数求导法 ln y = (1/2) ln(x^2+4x) - (1/3) ln (x^3+2)
y' / y = (1/2) ( 2x+4) /(x^2+4x) - (1/3) 3x^2 / (x^3+2)
y' = y * [ (x+2) /(x^2+4x) - x^2 / (x^3+2) ]
即 y' = (x^2+4x)^(1/2) / (x^3+2) ^1/3 * [ (x+2) /(x^2+4x) - x^2 / (x^3+2) ]