Find dy/dx when y=3(4^x)?

The easiest way to deal with a base other than e is to take logs:
ln y = ln 3 + x ln 4, and differentiate by the chain rule:
(1/y) * dy/dx = ln 4
So dy/dx = y ln 4 = 3 ln 4 * 4^x

y = 3(4^x)

dy/dx = (d/dx)[3(4^x)]
= 3 (d/dx)(4^x)
= 3 * 4^x ln(4)

log y = log 3 + x log 4
(1/y) dy/dx = log 4
dy/dx = 3^(4x) log 4