If `x = rcostheta,y= r sin theta`, show that

If x= cos theta , y= sin^3 theta , show that y ( d^2 y)/(d x^2 ) + (dy/dx)^2 = 3 sin^2 theta (5 cos^2 theta - 1)

If x= a cos theta , y= b sin theta , show that ( d^2 y)/(d x^2 ) = - b^4 /a^2y^3

If x= cos theta , y= sin^3 theta , show that y( d^2 y)/(d x^2 ) + (dy/dx)^2 = 3 sin^2 theta (5 cos^2 theta - 1)

If x=r cos theta, y=r sin theta Prove that x^(2)+y^(2)=r^(2)

If x = r cos theta, y = r sin theta then prove that (del (x, y)) / (del (r, theta)) xx (del (r, theta)) / (del (x, y)) = 1

If x= r cos theta, y = r sin theta , then (del r)/(del x) =_________

If x = r cos theta, y = r sin theta, Find (del (x, y)) / (del (r, theta)), (del (r, theta)) / (del (x, y))

If x = r cos theta, y = r sin theta, r =a(1+cos theta) then find (dy)/(dx)