Question

三道非常简单的微积分题，不费时间~

请帮忙解解，谢谢啦~

Answer 1

点击放大,再点击再放大.

（已经传上，稍等几分钟即可）

Answer 2

1 z=e^(yln(1+xy))
ðz/ðy=e^(yln(1+xy))*[ln(1+y)+y*1/(1+xy)*x]=(1+xy)^y*[ln(1+y)+xy/(1+xy)]

2 ðz/ðx=1/[1+(x+y)^2/(1-xy)^2]* [(1-xy+y(x+y))/(1-xy)^2]
=(1-xy)^2/[1+x^2y^2+x^2+y^2]*(1+y^2)/(1-xy)^2
=1/[(1+x^2)(1+y^2)]*(1+y^2)=1/(1+x^2)

同理可得ðz/ðy=1/(1+y^2)

3 dz/dt=dz/dx*dx/dt+dz/dy*dy/dt=e^(x-2y)cost-2e^(x-2y)*3t^2
=e^(x-2y)[cost-6t^2]=z(cost-6t^2)
ddz/(dt)^2=d(e^(x-2y)(cost-6t^2))dt=(cost-6t^2)*dz/dt+zd(cost-6t^2)/dt
=z(cost-6t^2)^2+z*(-sint-12t)
=z[(cost)^2-12t^2cost+36t^4-12sint-12t]