Download Review 7-2 - Hollie Teague

REVIEW 7-2
Find the derivative:
3
----3x - 4
1. f(x) = ln(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
f '(x) = -----1+x
+
4x
-------1 + x2
+
9x2
-------1 + x3
3. y = ln(cosx + 8x)
4. y = ln(ln12x)
5. y = 9xln2x
-sinx + 8
cosx + 8x
1
__x__
ln12x
=
1__
xln12x
9x(1/x) + 9ln2x
9 + 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) = 7
x2 + 2x - 8 = 7
x2 + 2x - 15 = 0
(x - 3)(x + 5) = 0
x = 3 or x = -5
9. Solve the equation.
e3x + 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 40 - 2
10. Solve for y:
ln y2 +3y - ln (y + 3) = 6
2 + 3y
y
ln
=6
y+3
ln(y) = 6
y = e6
SIMPLIFY:
11. ln(e3x)
3x
13.
eln7x+9
eln7x + e9
7xe9
12. e2ln5x
(5x)2 = 25x2
_1_
14. ln( 2x )
e
-2x