Posted by Rebecca on Thursday, December 2, 2010 at 8:25pm.
Use logarithmic differentiation to find dy/dx.
y = sq. root [(x^2  1)/(x^2 + 1)]

Calc  MathMate, Thursday, December 2, 2010 at 10:06pm
y = sq. root [(x^2  1)/(x^2 + 1)]
take log (to base e, =ln) on both sides
log(y) = (1/2)(log(x²1)log(x²+1)
differentiate with respect to x
dy/dx / y = x/(x²1)x/(x²+1)
= 2x/((x²1)(x²+1))
dy/dx = x/(x²1)x/(x²+1)
= 2x/((x²1)(x²+1)) * √(x²1)/√(x²+1)
Simplify.