设z=arctan(uv),而u=e^x,v=x^3,求dz⼀dx 解题过程

2024-12-23 14:19:02
推荐回答(1个)
回答1:

tan(z) = uv = x^3 e^(x)
dtan(z)/dx = sec^2(z) dz/dx = 3x^2e^(x)+x^3e^(x)
解出:
dz/dx = x^2(3+x)e^(x)/sec^2(z) //: 1+tan^2(z)=sec^2(z)
= x^2(x+3)e^(x)/[1+x^6 e^(2x)]