If y=` tan ^-1((ax-b)/(bx+a)) " then prove that " du/dx=1/(1+x^2).`

Explanation

To prove that \(\frac{dy}{dx} = \frac{1}{1+x^2}\) for the given function \(y = \tan^{-1}\left(\frac{ax-b}{bx+a}\right)\), we will follow these steps:

### Step 1: Rewrite the function
Given:
\[ y = \tan^{-1}\left(\frac{ax-b}{bx+a}\right) \]
We can simplify this expression by dividing both the numerator and the denominator by \(a\):
...