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Posted by 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 - , 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(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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