Question

求多元函数的微积分，z=x^y，而x=e^t，y=t，求dz/dt

谢谢，求步骤

Answer 1

z'x=yx^(y-1),z'y=x^ylnx
x't=e^t,y't=1
dz/dt=z'x*x't+z'y*y't=yx^(y-1)e^t+x^ylnx

追问

最后答案是dz/dt=2te^(t^2)，是在你最后得出的式子上进一步化简么？谢谢

追答

yx^(y-1)e^t+x^ylnx
代入x=e^t，y=t
=t(e^t)^(t-1)*e^t+(e^t)^t*t
=te^(t^2)+e^(t^2)*t
=2te^(t^2)

记得采纳哦