Question

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.

Answer 1

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]