If `x=rcostheta,y=rsintheta`, Find `(del(x,y))/(del(r,theta)), (del(r,theta))/(del(x,y))`

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 and y = r sin theta, prove that (del ^ (2) r) / (del x ^ (2)) + (del ^ (2) r) / (del y ^ (2)) = (1) / (r) [((del r) / (del x)) ^ (2) + ((del r) / (del y)) ^ (2)]

If V(x,y) = e^(x) (x cos y - y siny) , then prove that (del^(2)V)/(del x^(2)) + (del^(2) V)/(del y^(2)) =0

A function f (x,y) is said to be harmonic if (del^(2)f)/(del x ^(2)) + (del^(2)f)/(dely^(2)) =

If u=x^y then find (del u)/(del x) and (del u)/(del y) .

If w(x,y) = xy + sin(xy) , then prove that (del^(2) w)/(del y del x) = (del^(2) w)/(del x del y)

If u=ax-by , then ((del u)/(del y))=