logarithmic differentiation

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y= 4th root (x^2+1)/(x^2-1)

  • logarithmic differentiation -

    y = [(x^2 + 1)(x^2-1) ]^(1/4)
    = (x^4 - 1)^(1/4)
    ln y = (1/4) ln(x^4 -1)
    (dy/dx) / y = (1/4)(4x^3)/(x^4 - 1)
    dy/dx = (1/4)(y)(4x^3)/(x^4 - 1)
    or
    you can replace y with (x^4 - 1)^(1/4)
    and simplify that a bit since the denominator is x^4 - 1

  • logarithmic differentiation -

    Do you want the derivative of that? Does the "fourth root" apply to the numerator only, or the complete fraction
    (x^2+1)/(x^2-1) ?

    You need to write the function in a clear nonambiguous manner, using parentheses where necessary. Use ^1/4 for fourth roots.

  • missed the division sign - logarithmic differentiation -

    Sorry ana, my answer is incorrect,
    I read that as a multiplication , should have been a division

    ln y = (1/4) (ln (x^2 + 1) - ln(x^2 -1)

    (dy/dx) / y = (1/4) ( 2x/(x^2+1) - 2x/(x^2 + 1) )
    dy/dx = (1/4)(y) (4x)/(x^4 - 1)
    = xy/(x^4 - 1)

    replace y with the original if you have to.

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