REVIEW 7 2 Find the derivative 1 fx

REVIEW 7 -2

Find the derivative: 1. f(x) = ln(3 x - 4) 3 ----- 3 x - 4 2. f(x) = ln[(1 + x)(1 + x 2)2(1 + x 3)3 ] ln(1 + x) + ln(1 + x 2)2 + ln(1 + x 3)3 ln(1 + x) + 2 ln(1 + x 2) + 3 ln(1 + x 3) 1 4 x 9 x 2 f '(x) = ------ + -------- 1 + x 2 1 + x 3

3. y = ln(cosx + 8 x) 4. y = ln(ln 12 x) 5. y = 9 xln 2 x -sinx + 8 cosx + 8 x 1 __x__ ln 12 x = 1__ xln 12 x 9 x(1/x) + 9 ln 2 x 9 + 9 ln 2 x

6. y = ex 2 7. y = sin(e 3 x).

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) = 7 x 2 + 2 x - 8 = 7 x 2 + 2 x - 15 = 0 (x - 3)(x + 5) = 0 x = 3 or x = -5

9. Solve the equation. e 3 x + 2 = 40 ln e 3 x + 2 = ln 40 (3 x + 2) ln e = ln 40 Remember that ln e = 1. 3 x + 2 = ln 40 3 x = ln 40 - 2

10. Solve for y: ln y 2 +3 y - ln (y + 3) = 6 2 + 3 y y ln =6 y+3 ln(y) = 6 y = e 6

SIMPLIFY: 11. ln(e 3 x) 3 x 13. eln 7 x+9 eln 7 x + e 9 7 xe 9 12. e 2 ln 5 x (5 x)2 = 25 x 2 _1_ 14. ln( ) e 2 x -2 x