Finding a derivative with imaginary numbers?

Using Eulers idenity, $f(x)=i^x=e^{\frac{i\pi x}{2}}$

$\therefore f'(x)=\frac{1}{2}i\pi e^{\frac{i\pi x}{2}}=\frac{1}{2}i\pi i^x$

The correct answer is $\boxed {E}$