How to Simplify and Find Derivative with Complex Fractions?

[surferbarney0729]

question is...

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

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

 

[Robert1986]

That's what I would do.

 

[surferbarney0729]

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

 

[Mark44]

(1-x)s factor?

What are you asking?

Any tips on a start, self teaching calculus is difficult

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.

 

[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.

 

[surferbarney0729]

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

 

[mathnoobie]

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

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

 

[surferbarney0729]

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

 

[surferbarney0729]

2
(1-x)^2 - 2

 

[eumyang]

2
(1-x)^2 - 2

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

 

[mathnoobie]

2
(1-x)^2 - 2

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

 

[Mark44]

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?

 

[surferbarney0729]

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

 

[surferbarney0729]

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

 

[mathnoobie]

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

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.

 

[micromass]

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

Here's a LaTeX guide: https://www.physicsforums.com/showthread.php?p=3977517&posted=1#post3977517

 

[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

 

[mathnoobie]

-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

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))

 

[surferbarney0729]

ok thanks

 

[eumyang]

-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

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?

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

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

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.

 

[mathnoobie]

I feel like you just want the answer, rather than the help. If that's so you can check your answers in wolframalpha.com. It will spit out answers for you.

 

[Curious3141]

Test:

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

OK, this free Chrome plug-in called "Daum Equation Editor" works quite well for those who haven't the first clue about LaTeX. It's got buttons for fraction formatting, logarithms, etc.

EDIT: And I guess this was the original problem, also formatted via Daum editor. Wanted to test the "itex" tags too: \frac { 1 }{ 2 } \ln { (2x+\frac { 1 }{ 1-x } -4x+\frac { x }{ 1-x } +2x) }.

 

[Mark44]

And I guess this was the original problem, also formatted via Daum editor. Wanted to test the "itex" tags too: \frac { 1 }{ 2 } \ln { (2x+\frac { 1 }{ 1-x } -4x+\frac { x }{ 1-x } +2x) }.

At 23 posts in this thread we shouldn't have to still be asking what the OP meant in the first post.

 

[Curious3141]

At 23 posts in this thread we shouldn't have to still be asking what the OP meant in the first post.

Yes, I agree. I hope the OP formats his actual question using the editor I suggested - it's freely available, after all.