Question

find equation to tangent y=(pi*sqrt(x))/2 at x=1

Answer 1

Have you considered the 1st Derivative?

Answer 2

^Beat me to it. Take the first derivative of your original equation, then f'(1) will give you the y-coordinate you need.

Answer 3

f(x+h) - f(x)
f '(x) = Lim ───────
h→0 h

this is the formula you can use.
The result is the slope of the tangent line, and the point is just (1, f(1) )