REVIEW 7-2

Find the derivative:

 1. f(x)  =  ln(3x - 4)

         3       -----                            3x - 4  

  2. f(x)  =  ln[(1 + x)(1 + x2)2(1 + x3)3 ]

ln(1 + x) + ln(1 + x2)2 + ln(1 + x3)3 

ln(1 + x) + 2 ln(1 + x2) + 3 ln(1 + x3)

                         1                 4x                   9x2          f '(x)  =   ------     +     --------      +     --------                           1 + x            1 + x2             1 + x3

3. y = ln(cosx + 8x) -sinx + 8cosx + 8x

4. y = ln(ln12x) 1__x__ln12x

1__ xln12x=

5. y = 9xln2x

9 + 9ln2x

9x(1/x) + 9ln2x

6. y = ex2

7. y = sin(e3x).

SOLVE:8. ln (x + 4) + ln (x - 2) = ln 7

ln (x + 4)(x - 2) = ln 7

eln (x + 4)(x - 2) = eln 7

(x + 4)(x - 2) = 7x2 + 2x - 8 = 7

x2 + 2x - 15 = 0(x - 3)(x + 5) = 0x = 3 or x = -5

9. Solve the equation.e3x + 2 = 40

ln e 3x + 2 = ln 40

(3x + 2) ln e = ln 40Remember that ln e = 1.

3x + 2 = ln 40

3x = ln 40 - 2

10. Solve for y:

ln y2 +3y - ln (y + 3) = 6

y2 + 3yy + 3

ln = 6

ln(y) = 6y = e6

SIMPLIFY:11. ln(e3x) 12. e2ln5x

13. eln7x+9 14. ln( )

_1_e2x

3x (5x)2 = 25x2

eln7x + e9

7xe9-2x