To find: The equation of the tangent line.
First you need to find out m=dydx. Differentiate both side of xey+yex=1, with respect to x, we get
(xeydydx+ey)+(yex+exdydx)=0 ⇒ (xey+ex)dydx+(ey+yex)=0. Then m=dydx=−(ey+yex)ex+xey. Substitute x=0, we get m=ey+y. Now substitute x0=0 and y0=1 in the following equation: y−y0=m(x−x0) , we get y−1=−(ey+y)(x−0) y−1=−x(ey+y), which is the equation of tangent to the curve xey+yex=1 at the point (0,1).