The question is asking to find the first derivative of the composition (fogoh)(x). Given:

$\displaystyle f(x) = \sqrt{x^2-1}$

$\displaystyle g(x) = (x^3+5)^{17} $

$\displaystyle h(x) = \frac{2}{x}$

Computing for the derivatives I got:

$\displaystyle f'(x) = \tfrac{1}{2}(x^2-1)^{\frac{-1}{2}}(2x)$

$\displaystyle g'(x) = 17{(x^3+5)}^{16}(3x)$

$\displaystyle h'(x) = -2(2x)$

I understand that the derivative of $\displaystyle f(g(h(x))) = [f'(g(h(x)))].[g'(h(x))].[h'(x)]$ so I just need to plug the functions but I am not getting the right answer. Can someone please take me through the process step by step so I can see where I went wrong? I understand this is a long question but it would be greatly appreciated! Thank you!