Question

全导数:设z=arctan(xy),而y=e*x次方,求dz/dx

设z=arctan(xy),而y=e*x次方,求dz/dx,详细解答,谢谢

Answer 1

即z=arctan(xe^x)
dz/dx={1/[1+(xe^x)²]}*(xe^x)'
=(e^x+xe^x)/[1+(xe^x)²]

Answer 2

dz/dx=1/(1+(xy)^2)*(y+xy')
=(e^x+xe^x)/(1+(xe^x)^2)