Hyperbolic Thinking

Start by looking at the values of $A^2(x), B^2(x), A(2x), B(2x), A(x)B(x)$ and see if you can spot any simple relationships linking them.

To differentiate the two functions use the expression
$$\frac{d}{dx}\left(a^x\right) = \ln(a) a^x$$

Consider simple values of the functions, such as $n\pi$ and $\pm 1$.