If `f(x)=sqrt(x^2+1),\ \ g(x)=(x+1)/(x^2+1)` and `h(x)=2x-3` , then find `f^(prime)(h^(prime)(g^(prime)(x)))` .

Explanation

To find \( f'(h'(g'(x))) \) given the functions \( f(x) = \sqrt{x^2 + 1} \), \( g(x) = \frac{x + 1}{x^2 + 1} \), and \( h(x) = 2x - 3 \), we will follow these steps:

### Step 1: Find \( g'(x) \)

Using the quotient rule, which states that if \( g(x) = \frac{u}{v} \), then \( g'(x) = \frac{u'v - uv'}{v^2} \):

- Let \( u = x + 1 \) and \( v = x^2 + 1 \).
- Then, \( u' = 1 \) and \( v' = 2x \).
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