# Just look carefully!

Calculus Level 5

Let $$f$$ be a twice differentiable function defined on $$x>0$$ satisfying $$x f(y) + y f(x) = f(xy)$$ for all $$x,y> 0$$. Given that $$f'(1) = 1$$, find $$\displaystyle 4\sum_{x=1}^\infty f''(x) f''(x+2)$$.

×