# Simplify and find derivative

1. Jul 24, 2012

### surferbarney0729

question is...

(ln(2x+1/(1-x)-4x+x/(1-x)+2x))/2

I start by simplifying and then finding the derivative...correct?

2. Jul 24, 2012

### Robert1986

That's what I would do.

3. Jul 24, 2012

### surferbarney0729

(1-x)s factor? Any tips on a start, self teaching calculus is difficult

4. Jul 24, 2012

### Staff: Mentor

Just so we're all starting on the right page, is this what you're working with, as what you're taking the natural log of?

$$2x + \frac{1}{1 - x} - 4x + \frac{x}{1 - x} + 2x$$

What you wrote is (1/2)ln(y), with y being the expression above.

5. Jul 24, 2012

### mathnoobie

Simplifying gives you a simple log to derive.
Recall that division inside of logs means subtraction of top and bottom.
That should give you a simpler derivative to take in my opinion.

6. Jul 24, 2012

### surferbarney0729

I am just looking for help on how to solve the problem.

7. Jul 24, 2012

### mathnoobie

I don't think anymore help can be given without giving the answer away.

8. Jul 24, 2012

### surferbarney0729

ok, ill solve it. Hopefully someone will verify the answer I find and let me know if I am right

9. Jul 24, 2012

### surferbarney0729

2
(1-x)^2 - 2

10. Jul 24, 2012

### eumyang

You should learn to use LaTeX. Is the above supposed to be this?
$$\frac{2}{(1 - x)^2 - 2}$$

11. Jul 24, 2012

### mathnoobie

The denominator is ((1-x)^2-2)
=x^2-2x-1
correct?
If so, try re-checking your algebra.

12. Jul 24, 2012

### Staff: Mentor

I don't think that's right, but I'm not sure what the problem is, since you didn't answer the question I asked in post #4.

The title of your post is "Simplify and find derivative" so I assume that the problem is to simplify the expression and then take its derivative.

What do you get when you simplify the expression, before you take its derivative?

13. Jul 24, 2012

### surferbarney0729

2(x^2-2x+2)/(1-x)

14. Jul 24, 2012

### surferbarney0729

i am looking into LaTex, I apologize for my mathematical formatting computer skills

15. Jul 24, 2012

### mathnoobie

This is quite vague, is that the simplification?
If the inside of your log looks like what what mark posted, then the 2x, 2x, and 4x, all cancel out.
The last remaining terms have common denominators so you can add them.

16. Jul 24, 2012

### micromass

Staff Emeritus
17. Jul 24, 2012

### surferbarney0729

-2x+2+2/(1-x)

derivative = -2 + 2/(1-x)^2

I am driving many of you nuts and I thank you for your patience

18. Jul 24, 2012

### mathnoobie

Derivative of that is correct, but isn't it inside of a natural log, and according to the original equation that was given, the simplification would be
ln((1+x)/(1-x))

19. Jul 24, 2012

### surferbarney0729

ok thanks

20. Jul 24, 2012

### eumyang

Yes, you are driving us nuts, because you are not being clear in who you are replying to (or you do not completely answer someone's question), and because you show only snippets of work, not the whole thing.

First thing (and Mark44 asked this already), is this what is supposed to be inside the natural log? Yes or no?
$2x + \frac{1}{1 - x} - 4x + \frac{x}{1 - x} + 2x$

Second, where did the bolded come from?
If the bolded is supposed to be a simplification of the LaTeX I wrote above, then it's wrong. Show us all of your work. Be clear and precise. Otherwise, people won't want to help you.