derivative

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41) Find the derivative.

h(x)= (3x^2 + 1)^3 / (x^2 - 1)^4

This is where I am at the moment....

h'(x)= (x^2-1)^4 (3)(3x^2+1)^2(6x) - (3x^2+1)^3(4)(x^2-1)^3(2x)

This is what I am trying to get....(not final answer)

=2x(x^2-1)^3(3x^2+1)^2[(9)(x^2-1) - (4)(3x^2+1)}



Am really struggling with this. I have the answer in the back of the book but am not getting it right. have the solutions manual also. The chapter is on general power rule and chain rule.

  • derivative -

    h(x)= (3x^2 + 1)^3 / (x^2 - 1)^4
    rewrite as
    h(x)= (3x^2 + 1)^3 * (x^2 - 1)^-4

    first*derivative second + second*derivative first

    h' = (3x^2 + 1)^3*(-4)(x^2 - 1)^-5 (2x)
    +(x^2 - 1)^-4 *(3)(3x^2 + 1)^2 (6x)

    =(3x^2 + 1)^2(x^2 - 1)^-4 [-8x(3x^2 + 1)(x^2 - 1)^-1 +12x]

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