# Help with Logarithmic Differentiation

1. Jul 16, 2012

### communitycoll

1. The problem statement, all variables and given/known data
y = [2x + 1]^5 * [(x^4) - 3]^6

2. Relevant equations
I take the derivative of the natural log of both sides:

(y' / y) = [(10 ln(2x + 1)^4) / (2x + 1)] + [(24x^3 ln(x^4 - 3)^5) / (x^4 - 3)]

then I multiply both sides by the original function:

y' = [((10 ln(2x + 1)^4) / (2x + 1)) + ((24x^3 ln(x^4 - 3)^5) / (x^4 - 3))] * [(2x + 1)^5 * ((x^4) - 3)^6]

My book, however, says the answer is:

y' = [(10 / (2x + 1)) + (24x^3 / (x^4 - 3))] * [(2x + 1)^5 * ((x^4) - 3)^6]

^ i.e., the same thing without the logs.

Could someone please explain what I did wrong, or where I might have gone wrong?

3. The attempt at a solution
What you see above.

2. Jul 16, 2012

### SammyS

Staff Emeritus
It's helpful to do the problem in steps.

What did you get for ln(y) ?

Then, what did you get for the derivative of that result?

3. Jul 16, 2012

### communitycoll

I got ln(y) for ln(y), I'm not sure I understand the first question.

The derivative of that I got:

(1 / y)(y')

4. Jul 16, 2012

### Villyer

I think that you took your derivitives wrong.

I see that you broke it up into the sum of two logs, but remember that they are of the form ln(u^n) and not of the form ln(u)^n.

5. Jul 16, 2012

### communitycoll

I use chain rule on each of those logs; should I not?

6. Jul 16, 2012

### communitycoll

Ah, forget I asked anything. I understand what I did wrong. Thanks anyway.

7. Jul 16, 2012

### SammyS

Staff Emeritus
If y = [2x + 1]5 * [(x^4) - 3]6, then ln(y) = __?__ .

8. Jul 17, 2012

### Staff: Mentor

Is there a reason you didn't apply the relationship for the derivative of the product of two functions? Did the question constrain you to use logarithmic differentiation?