Use logarithmic differentiation to find dy/dx.

Question

y = sq. root [(x^2 - 1)/(x^2 + 1)]

Answer 1

y = sq. root [(x^2 - 1)/(x^2 + 1)]

take log (to base e, =ln) on both sides
log(y) = (1/2)(log(x²-1)-log(x²+1)

differentiate with respect to x
dy/dx / y = x/(x²-1)-x/(x²+1)
= 2x/((x²-1)(x²+1))

dy/dx = x/(x²-1)-x/(x²+1)
= 2x/((x²-1)(x²+1)) * √(x²-1)/√(x²+1)

Simplify.