List of top Mathematics Questions on Derivatives of Functions in Parametric Forms asked in CBSE Class XII

If \( x = a(\sin t - t \cos t) \) and \( y = b(\cos t + t \sin t) \), then find \( \frac{dy}{dx} \) and \( \frac{d^2y}{dx^2} \).

If \( x = e^{t + \frac{1}{t}} \) and \( y = e^{t - \frac{1}{t}} \), then find \( \frac{dy}{dx} \) at \( t = -2 \).

If \( x = \sin t - \cos t \) and \( y = \sin t \cos t \), find the value of \(\frac{dy}{dx}\) evaluated at \( t = \frac{\pi}{4} \).