List of top Mathematics Questions on Differentiation of Parametric Functions

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

If \( x = e^{\sin^{-1} t}, y = e^{\cos^{-1} t} \), find \( \frac{dy}{dx} \) at \( t = \frac{1}{\sqrt{2}} \).

Let f: [a, b]R be a continuous function on [a, b] and differentiable on (a, b), then there exists some e in (a, b) such that
\(f'(c) = \frac{f(b)-f(a)}{b-a}\)
This theorem in named