How do you differentiate 2^x?

We can differentiate this implicitly by writing the question as:y = 2^x Then we take the log of both sides:ln(y) = ln(2^x)Using the rules of logartithms this can be written as:ln(y) = x ln(2)Now we can differentiate this easily:y^-1 dy/dx = ln(2)We can now re-arrange to get:dy/dx = y ln(2)And finally we can substitute y to get our answer:dy/dx = 2^x ln(2)So we have shown that the derrivative of 2^x is simply 2^x multiplied by ln(2)