If `x=a (cos t +t sin t)" and "y= a (sin t -t cos t)`, find `(d^(2)y)/(dx^(2))`.

If x =a ( cos t + t sin t), y = a [sin t-t cos t] then find dy/dx .

If x=a(cost+1/2logtan^2t) and y=asint then find (dy)/(dx) at t=pi/4

x= 2 cos t -cos 2t ,y=2 sin t-sin 2t Then the value of (d^(2)y)/(dx^(2)) at t=pi/2

Find (dy )/(dx) if x=a ( t - sin t), y = a (1 - cos t).

Find (dy)/(dx) if x =a ( t - sin t), y =a (1- cos t)

If w(x,y,z) =x^(2) + y^(2)+ z^(2), x=e^(t), y=e^(t) sin t and z=e^(t) cos t , find (dw)/(dt) .

If a curve is represented parametrically by the equation x=f(t) and y=g(t)" then prove that "(d^(2)y)/(dx^(2))=-[(g'(t))/(f'(t))]^(3)((d^(2)x)/(dy^(2)))