I tried typing the following to find if the function is continuous at (0,0) and a possible step by step solution:
continuity of
d(piecewise[{{(x^2+y^2)sin(1/sqrt(x^2+y^2)),(x,y)!=(0,0)}, {0, (x,y)=(0,0)}}])/dx at (0,0)
but this query only calculates the inner expression