Here is a similar problem worked out for you:
d
dx |
|
3x - 1
2x- 1 |
|
5 |
Since the CTE tells us that we have a quantity raised to the 5, we should use the chain rule in the following form:
d
dx |
u5 |
= |
5u4 |
du
dx |
Therefore,
d
dx |
|
3x - 1
2x- 1 |
|
5 |
= |
| 5 |
|
3x - 1
2x- 1 |
|
4 |
d
dx |
|
3x - 1
2x- 1 |
|
|
|
|
|
|
|
= |
| 5 |
|
3x - 1
2x- 1 |
|
4 |
|
3(2x- 1) - (3x-1)(2)
(2x- 1)2 |
|
By the quotient rule |
|
|
|
|
|
|
= |
| 5 |
|
3x - 1
2x- 1 |
|
4 |
|
-1
(2x- 1)2 |
|
Simplify |
|
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