The left hand derivative of $f(x)=[x]\sin(\pi x)$ at $x=k$, where $k$ is an integer is

Question

$\begin{array}{1 1}(a)\;(-1)^k(k-1)\pi&(b)\;(-1)^{k-1}(k-1)\pi\\(c)\;(-1)^kk\pi&(d)\;(-1)^{k-1}k\pi\end{array}$