设z=arctan(uv),而u=e^x,v=x^3,求dz/dx
问题描述：
设z=arctan(uv),而u=e^x,v=x^3,求dz/dx
答
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)]