text: y = 2^x\n\nln y = ln 2^x\n\nd/dx ln y = d/dx ln 2^x\n\nd/dx ln y = d/dx x*ln 2\n\nPull the constant (ln 2) out:\n\ny'/y = ln 2 * d/dx x\n\ny'/y = ln 2\n\ny' = y * ln 2\n\ny' = 2^x * ln 2\n\n*** Remember this advice, kids.  Whenever you want to get rid of a variable exponent during differentiation, use logarithmic differentiation.  Using it will make things cleaner and easier.