# Math Help - Derivative, Chain Rule Problem. Help Plz!!

1. ## Derivative, Chain Rule Problem. Help Plz!!

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

$f(x) = \sqrt{x^2-1}$
$g(x) = (x^3+5)^{17}$
$h(x) = \frac{2}{x}$

Computing for the derivatives I got:

$f'(x) = \tfrac{1}{2}(x^2-1)^{\frac{-1}{2}}(2x)$
$g'(x) = 17{(x^3+5)}^{16}(3x)$
$h'(x) = -2(2x)$

I understand that the derivative of $f(g(h(x))) = [f'(g(h(x)))].[g'(h(x))].[h'(x)]$ 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!

2. f ' is correct but g ' and but h ' aren't

g= (x^3 + 5)^17

g ' = 17(x^3 +5)^16 (3x^2)

h = 2/x = 2x^(-1)

h' = -2 x^(-2) = -2/(x^2)

Try it now