The function $\displaystyle f:R^2-->R $ is defined by $\displaystyle

f(x,y) = \frac{sin(x^2y)}{x^2+y^2} , if (x,y)\neq(0,0) $

$\displaystyle = 0 , if (x,y)\neq(0,0)$

then the function

(a) is differentiable at $\displaystyle (0,0) $

(b) is continuous at $\displaystyle (0,0) $, but not differentiable

(c) is not continuous at $\displaystyle (0,0) $

(d) has continuous partial derivatives at $\displaystyle (0,0) $