Differentiate the following functions with respect to x:

sin²(2x + 1)

Show that of all the rectangles of given area, the square has the smallest perimeter.

Find the value of a and b such that the following function f(x) is a continuous function:

If x sin (a + y) + sin a cos (a + y) = 0, prove that

The function f(x) = e^|x| is

Show that of all the rectangles with a given perimeter, the square has the largest area.

If the function f (x) given by

is continuous at x =1, find the values of a and b.

Find when x and y are connected by the relation given

(x² + y²)² = xy

Let f(x) = |sinx|. Then

The derivative of cos^-1(2x² – 1) w.r.t. cos^-1 x is