Take log of both sides
\(\ln y = \ln(2^{\sin \pi x})\)
Use log property to get "x" out of the exponent
\(\ln y = (\ln 2) (\sin \pi x)\)
Differentiate
\(\frac{dy}{y} = (\pi \ln 2)(cos \pi x) dx\)
Move y to Right side (Note y = original expression)
\(\frac{dy}{dx} = (\pi \ln 2) (\cos \pi x) 2^{\sin \pi x}\)
In general, whenever you have a function in the form
\(y = a^{f(x)}\)
The derivative will be
\(\frac{dy}{dx} = (\ln a) (f'(x))a^{f(x)}\)
