z=(u^2)v,u=e^t,v=cost,求dz/dt
问题描述：
z=(u^2)v,u=e^t,v=cost,求dz/dt
答
dv=dcost=-sintdt du=d(e^t)=e^tdt dz=d((u^2)v)=(u^2)dv+vd(u^2) =(u^2)dv+2uvdu =u^2(-sint)dt+2uve^tdt =-e^(2t)sintdt+2e^(2t)costdt =e^(2t)(cost-sint)dt dz/dt=e^(2t)*(cost-sint)