Let `g(x)={(x^2+xtanx-xtan2x)/(a x+tanx-tan3x),x!=0 0,x=0` If `g^(prime)(0)` exists and is equal to nonzero value `b ,` then `52 b/a` is equal to _____

Explanation

To solve the problem, we need to find the derivative \( g'(0) \) and express it in terms of \( a \) and \( b \). Let's go through the steps systematically.

### Step 1: Define the function \( g(x) \)
The function is defined as:
\[
g(x) =
\begin{cases}
\frac{x^2 + x \tan x - x \tan 2x}{ax + \tan x - \tan 3x}, & x \neq 0 \\
...