review 7-2. find the derivative: 1. f(x) = ln(3x - 4) 3 ----- 3x - 4 2. f(x) = ln[(1 + x)(1 + x2) 2...
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![Page 1: 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](https://reader036.vdocument.in/reader036/viewer/2022082518/56649e3f5503460f94b2fbf1/html5/thumbnails/1.jpg)
REVIEW 7-2
![Page 2: 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](https://reader036.vdocument.in/reader036/viewer/2022082518/56649e3f5503460f94b2fbf1/html5/thumbnails/2.jpg)
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
![Page 3: 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](https://reader036.vdocument.in/reader036/viewer/2022082518/56649e3f5503460f94b2fbf1/html5/thumbnails/3.jpg)
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
![Page 4: 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](https://reader036.vdocument.in/reader036/viewer/2022082518/56649e3f5503460f94b2fbf1/html5/thumbnails/4.jpg)
6. y = ex2
7. y = sin(e3x).
![Page 5: 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](https://reader036.vdocument.in/reader036/viewer/2022082518/56649e3f5503460f94b2fbf1/html5/thumbnails/5.jpg)
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
![Page 6: 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](https://reader036.vdocument.in/reader036/viewer/2022082518/56649e3f5503460f94b2fbf1/html5/thumbnails/6.jpg)
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
![Page 7: 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](https://reader036.vdocument.in/reader036/viewer/2022082518/56649e3f5503460f94b2fbf1/html5/thumbnails/7.jpg)
10. Solve for y:
ln y2 +3y - ln (y + 3) = 6
y2 + 3yy + 3
ln = 6
ln(y) = 6y = e6
![Page 8: 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](https://reader036.vdocument.in/reader036/viewer/2022082518/56649e3f5503460f94b2fbf1/html5/thumbnails/8.jpg)
SIMPLIFY:11. ln(e3x) 12. e2ln5x
13. eln7x+9 14. ln( )
_1_e2x
3x (5x)2 = 25x2
eln7x + e9
7xe9-2x