I'm having a difficulty differentiating this using L'Hospital's rule:

lim x->(infinite) xsin(pi/x)

Applying L'Hospital's rule and differentiating I got:

lim x->(infinite) xcos(pi/x) + sin(pi/x)

and that equals = (infinite)(1) + 0 = infinite

The correct answer in my textbook is just "pi"

Can someone tell me what I'm doing wrong?