Important formulas

d (a^b )/ dx  = 0                              This is a constant

d ( xⁿ ) / dx = nx^{n -1}                      Power Rule

d (a ^x ) / dx = a ^x ln a                     Derivative of an exponential function

d ( x ^x )/dx = x ^x (1 + ln x )            Logarithmic Differentiation

It is sometimes easy to get these several functions confused & use the wrong rule for differentiation.  Always remember that each rule has extremely particular rules for where the variable & constants must be.  For instance, the Power Rule needs that the base be a variable and the exponent are a constant, whereas the exponential function needs accurately the opposite.

If you can keep straight all of the rules you can't go wrong along with these.