List of top Mathematics Questions on Differentiability asked in MET

The solution of the equation \(\frac{dy}{dx} = \frac{x(2\log x + 1)}{\sin y + y\cos y}\) is

The curve for which the length of the normal is equal to the length of the radius vector, are

The set of points where the function \( f(x) = |x| \) is differentiable, is

If \( f(x) = |x| \sin |x| \), then \( f'(x) \) is equal to

\( x = \frac{1 - \sqrt{y}}{1 + \sqrt{y}} \implies \frac{dy}{dx} \) is equal to

\( x = \cos^{-1}\left(\frac{1}{\sqrt{1+t^{2}}}\right), \; y = \sin^{-1}\left(\frac{t}{\sqrt{1+t^{2}}}\right) \implies \frac{dy}{dx} \) is equal to

\( \frac{d}{dx} \left[ a \tan^{-1} x + b \log\left(\frac{x-1}{x+1}\right) \right] = \frac{1}{x^{4} - 1} \implies a - 2b \) is equal to