Problem 686 (difficulty: 4/10)

Assume that      (1)  \(\displaystyle x\cdot f(x), \ \ \ \ \)  (2)  \(\displaystyle f(x^3), \ \ \ \ \)  (3)  \(\displaystyle f^3(x)\)

is differentiable at 0. Does it imply that \(\displaystyle f(x)\) is differentiable at 0?

Give me another random problem!