# Calc

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Use logarithmic differentiation to find dy/dx.

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

• Calc -

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.

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