If \(y=\sqrt { x } +\frac { 1 }{ \sqrt { x } } \) show that \(2x\frac { dy }{ dx } +y=2\sqrt { x } \).

Show that the function f(x) = [x] where [x] denotes the greatest integer function is discontinuous at all integral points

Is the function defined by f(x) = x² -sin x + 5 is continuous at x =\(\pi\)?

Differentiate: \(\sin ^{ -1 }{ \left( \sqrt { \cos { x } } \right) } \)

Differentiate: sin² x + cos² y = 1.