If `y=btan^(-1)(x/a+tan^(-1)y/x)`,find`(dy)/(dx)dot`

Explanation

To solve the problem \( y = b \tan^{-1}\left(\frac{x}{a} + \tan^{-1}\left(\frac{y}{x}\right)\right) \) and find \( \frac{dy}{dx} \), we will follow these steps:

### Step 1: Rewrite the equation
We start by isolating \( \frac{y}{b} \):
\[ \frac{y}{b} = \tan^{-1}\left(\frac{x}{a} + \tan^{-1}\left(\frac{y}{x}\right)\right) \]

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