Partial Derivative

Consider the polar coordinate on R^2,i.e
x= rcosθ ; y = rsinθ
Compute the following partial derivatives in term of coordinate (r,θ)
a) ∂/∂x=?
b) ∂/∂y=?
c) ((∂^2)/(∂x^2))+((∂^2)/(∂y^2))=?

I know ∂/∂x= (∂/∂r)(∂r/∂x)+(∂/∂θ)(∂θ/∂x)
Is ∂r/∂x = cosθ and ∂θ/∂x = -rsinθ ?