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.