2^x + 2^y = 2^xy = 2^x * 2^y

2^y = (2^x + 2^y) / 2^x

y = log2 (2^x + 2^y) / 2^x

y' = (log2 (2^x + 2^y) / 2^x)' = 1 / ( (2^x + 2^y) / 2^x) * ln 2