Find `dy/dx` when `x = a (cos theta + theta sin theta)`, `y = a (sin theta - theta cos theta).`

If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find dy/dx : x = a(cos theta + theta sin theta), y = a(sin theta - theta cos theta)

Find dy/dx , if x and y are connected parametrically by the equations (without eliminating the parameter). x = a (cos theta + theta sin theta), y = a(sin theta - theta cos theta)

Find dy/dx when x = cos theta + cos 2 theta, y = sin theta + sin 2 theta)

Show that the normal at any point theta to the curve x = a cos theta + a theta sin theta, y = a sin theta - a theta cos theta is at a constant distance from the origin.

If x = a (cos theta + theta sin theta) and y = a (sin theta - theta cos theta) , find (d^2y)/(dx^2) at t = pi/4 .

Find dy/dx when x= a (theta + sin theta), y = a(1+cos theta)

If x = a(cos 2theta + 2theta sin 2theta) and y = a(sin 2theta - 2theta cos 2theta) ,find (d^2y/dx^2) at theta = π/8