SOLUTION: Given sin(y)=cos(x), find {{{dy/dx}}} at the point (3pi/2, 2pi)

(1)  Differentiate the given equation (both sides).  You will get

         cos(y)*dy = -sin(x)*dx




(2)  Substitute here  x= 3pi/2,  y= 2pi.  You will get

         cos(2pi)*dy = -sin(3pi/2)*dx,  or

         1*dy        = -(-1)*dx,   or

           dy        = dx.




(3)  Hence,   = 1.      ANSWER