Problem
Find all values of $a$ and $b$ that make the following function differentiable for all values of $x$: f(x) = \begin{cases} \arctan(ax+b), x<0\\ \pi/4e^{\sin(bx)}, x \geq 0\\ \end{cases}
I thought I had this question figured out but it started to get more complicated than I think it should be. Any help would be greatly appreciated, Thank you.