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 + x 2 ) 2 + ln(1 + x.

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Presentation transcript:

REVIEW 7-2

Find the derivative: 1. f(x) = ln(3x - 4) x f(x) = ln[(1 + x)(1 + x2) 2 (1 + x3) 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 4x 9x2 f '(x) = x 1 + x2 1 + x3

3. y = ln(cosx + 8x) -sinx + 8 cosx + 8x 4. y = ln(ln12x) 1 __x__ ln12x 1__ xln12x = 5. y = 9xln2x 9 + 9ln2x 9x(1/x) + 9ln2x

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

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

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

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

SIMPLIFY: 11. ln(e 3x )12. e 2ln5x 13. e ln7x ln( ) _1_ e 2x 3x (5x) 2 = 25x 2 e ln7x + e 9 7xe 9 -2x