z=u²v+3uv^4,u=e^x, v=sin x,求dz/dx,求各位大神解答啊→_→

题目

z=u²v+3uv^4,u=e^x, v=sin x,求dz/dx,求各位大神解答啊→_→

答案

z=u²v+3uv^4,u=e^x,v=sin x,求dz/dx
dz/dx=2uu'v+u^2v'+3u'v^4+3v(4v^3)v'
=2e^(2x)sinx + e^(2x)cosx +3e^x (sinx)^4 + 12(sinx)^4 cosx
=2sinx e^(2x) + cosx e^(2x) + 3(sinx)^4 e^x (e^x + 4cosx)
=2sinx e^(2x) + 3(sinx)^4 e^(2x) + cosx e^(2x)+12(sinx)^4 cosx e^(x)
=sinx e^(2x)[2+3(sinx)^3] + cosx e^x [e^x+12(sinx)^4]