SOLUCIONS DERIVADES

MATEMÀTIQUES APLICADES A LES C.S:
1. f ‘(x) = 15 x2 + 8x – 3
2. f ‘(x) =
2 + 1
3 x 33x2
.
.
3
3. f ‘(x) = (2x + 3) ln x + x + 3
4. f ‘(x) =
-11
(3x – 1 )2
.
5. f ‘(x) = – x2 – 6x + 11
(x2 – 3x + 2)2
6. f ‘(x) = 3 – 2x
ex
7. f ‘(x) = 4 (x2 + 3x – 2)3 · (2x + 3)
8. f ‘(x) = 2x (2x2 – 3)
x4 + 3x2 +2
9. f ‘(x) =
-3
(x + 2)(x – 1)
.
10. f ‘(x) = =
x
x2 + 1
.
x3 + 4x2 – 3x + 5
11. f ‘(x) = 4
· ln 4 · (3x2 + 8x – 3)
12. f ‘(x) = =
- 20
(3x – 2)(2x – 8)
.
13. f ‘(x) = (3x2 – 2) (x2 + 3) – 2x (x3 – 2x) ln (x3 – 2x)
(x3 – 2x) (x2 + 3)2
SOLUCIONS DERIVADES
14. f ‘(x) = – 96x3 – 27x2 = –3x2 (32x + 9)
5

4
15. f ‘(x) = 27  x
5
16. f ‘(x) = ex ( x2 + 2x – 1/x – lnx)
17. f ‘(x) = 6
x3
.
18. f ‘(x) = x ex lnx – ex – 3 = ex (x lnx – 1) – 3
x ln2x
x ln2x

19. f ‘(x) = 49 5 x2
5
20. f ‘(x) = – 96x3 + 81x2 – 3
21. f ‘(x) = – 5x4 –
(2ex +
22. f ‘(x) =
1
x ln5
.
1 ) lnx – ( 2ex + log7x)
x ln7
x
2
ln x
.
23. f’ (x) = x5 (6lnx – 1)
ln2x
24. f ‘(x) = 1 – x ln10·ln8·logx
x 8x ln10
25. f ‘(x) = – 6x2 – 70x + 15
(– 2x2 – 5)2
26. f ‘(x) = 4x ln4 + 1/x
27. f ‘(x) = 1/x
28. f ‘(x) = x (2 – xln7)
.
7x
29. f ‘(x) =
5
x ln6
30. f ‘(x) = 9x2 
.
1
3 x2
.
3
31. f ‘(x) =
4
33(4x – 5)2
.
32. f ‘(x) = 5x (ln5·lnx + 1/x)
33. f ‘(x) = e-x (x3 + 3x – x + 1) = x3 + 3x – x + 1
ex
34. f ‘(x) =
1
x·lnx·ln10
.
35. f ‘(x) = e · xe-1
x2 + 1
36. f ‘(x) = 2
·ln2·2x
37. f ‘(x) = 2x [ ln2 (ex + 3) + ex ]
38. f ‘(x) = 7x ( ln7·log5 x +
1 )
x ln5
.
39. f ‘(x) = 10·lnx – 10·logx·ln10
4x·ln2x·ln10
x2 + 2
40. f ‘(x) =
2
3x
+3
(x3 + 1) ln3
.
·ln3·2x