posted by Anonymous .
consider a point on a circle x2+y2=1.At what rate Y is changing with respect to X when the point is at X=1/2....
There are two points on the circle with x = 1/2:
(1/2, sqrt3/2) and (1/2,-sqrt3/2)
Which one are you talking about?
Anyway, what you want is dy/dx.
Use a ^ sign before exponents.
x^2 + y^2 = 1
Use implicit differentiation.
2x + 2y*dy/dx = 0
dy/dx = -x/y = -1/sqrt3 or 1/sqrt3
depending upon which of the two points you are talking about.