Math 151-copyright Joe Kahlig, 19C                                                               Page 1
                Section 3.6: Derivatives of Logarithmic Functions
                Derivative Formulas:
                y = ln(x)
                y = loga(x)
                Example: Find the derivative of these functions.
                             2
                A) y = ln(5x −1)
                             2
                            x     −5x
                B) y = ln(e   +e     )
                              7
                C) y = log4(x +3x)
                             2
                D) y = elog(x +1)
                Math 151-copyright Joe Kahlig, 19C                                                               Page 2
                                    2
                E) y = 5xlog(cot(x ))
                                   3   4     2
                F) y = log5 (x+4) (x +1)
                           5        
                             x +7
                G) y = ln   √
                             5  4
                              x +2
               Math 151-copyright Joe Kahlig, 19C                                                         Page 3
               Logarithmic Differentiation
               Example: Find the derivative.
                        cos(x)
               A) y = x
                               2x
                        3     e
               B) y = (x +7)
               Math 151-copyright Joe Kahlig, 19C                                                         Page 4
               Example: Find the derivative.
                      3    4  5     8
               y = (x +1) (x +2)
                          5     5
                       (6x +7)