Appeared in: 2026 (3 sets)
(a) If $xy = e^{x - y}$, then find $\frac{dy}{dx}$.
OR
(b) Differentiate $\tan^{-1} \left$ \frac{\sqrt{1 + x^2} - \sqrt{1 - x^2}}{\sqrt{1 + x^2} + \sqrt{1 - x^2}} \right$$ with respect to $\cos^{-1} x^2$.