Question

设f(x,y)=∫e^-t^2dt

设u=f(x,y)=∫(0到xy)e^(-t^2)dt 求du
答案是du=e^(-x^2*y^2)(ydx+xdy)

Answer 1

简单计算一下即可，答案如图所示

Answer 2

du=∂u/∂xdx+∂u/∂ydy
=e^(-x^2*y^2)∂(xy)/∂xdx+e^(-x^2*y^2)∂(xy)/∂ydy (利用对积分上限函数的求导)
=e^(-x^2*y^2)ydx+e^(-x^2*y^2)xdy
=e^(-x^2*y^2)(ydx+xdy)
祝你学业进步~