I having trouble figuring this problem out:

Find $\displaystyle f^\prime^\prime(2)$ for $\displaystyle tsin\frac{\pi}{t}$

So using the product rule, $\displaystyle f^\prime(t)= tcos\frac{\pi}{t}+sin\frac{\pi}{t}$

Using the sum rule, $\displaystyle f^\prime^\prime(t)=t(-sin\frac{\pi}{t})+cos\frac{\pi}{t}$

so plugging in $\displaystyle f^\prime^\prime(2)=2(-(1))+0=-2$

Does that seem right?

Any help is greatly appreciated!