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.

Differentiate: sin x.sin 2x. sin 3x with respect to 'x'.

Find \(\frac{dy}{dx}\) if x = 15(t - sin t); y = 18(1 - cos t).

If e^y (x + 1) = 1, show that \(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } ={ \left( \frac { dy }{ dx } \right) }^{ 2 }\)

Evaluate \(\underset { x\rightarrow -3 }{ lim } \frac { { x }^{ 3 }+27 }{ { x }^{ 5 }+243 } \)

Evaluate \(\underset { x\rightarrow 0 }{ lim } \frac { 2sinx-sin2x }{ { x }^{ 3 } } \)