Tricky Derivative - I need quick help

  • Thread starter dekoi
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In summary, the conversation is about finding the first derivative of the function f(x)=\frac{e^x(x^2+x+4)+e^{-x}(x^3-1)(x^8+1)}{(e^x+x^2+1)(x^6e^x+2)}, and various methods have been discussed including using product/quotient laws, logarithmic differentiation, and first principles. However, it is determined that
  • #1
dekoi
I am faced with the function:
[tex]f(x)=\frac{e^x(x^2+x+4)+e^{-x}(x^3-1)(x^8+1)}{(e^x+x^2+1)(x^6e^x+2)}[/tex]

Can anyone think of a QUICK, EFFECTIVE way of finding the first derivative of this function, in simplified form??

I have tried using the product/quotient laws, and I am now facing huge expanding! (The document is attached).
I am assuming that this is a very ineffective way of finding the derivative, so then I tried another method...
I used logarithmic differentiation, but I realized that in order to get it into simplified form I will have to do much factoring/expanding also.

Then I thought, maybe using first principles would be easier? But I haven't tried that method yet. I'm assuming it will also consist of a lot of expanding.

Without telling me to use "delta-epsilon" because I haven't learned that yet, how can I find this derivative?Thank you.
 

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  • #2
I would break it up and brute force it. I don't see any shortcuts.
 
  • #3
:eek:




Anyone else?... Please......
 
  • #4
I don't see anything that can be done to make this less painful.
 
  • #5
You might (??) gain some simplicity by multiplying out all of the polynomials before plug-n-chug...
 
  • #6
I guess I will have to...
 
  • #7
sometimes don't you just want to hug maple :)
 
  • #8

FAQ: Tricky Derivative - I need quick help

1. What is a derivative?

A derivative is a mathematical concept used to describe the rate of change of one variable with respect to another. In simpler terms, it is a measure of how much one quantity changes in relation to another quantity.

2. How do I solve a tricky derivative problem?

To solve a tricky derivative problem, you will need to use a combination of basic derivative rules and advanced techniques such as the chain rule, product rule, or quotient rule. It is also important to identify the appropriate variables and use correct notation.

3. What is the purpose of finding derivatives?

The purpose of finding derivatives is to analyze the behavior of a function and determine its rate of change at a specific point. It is also used in many real-world applications such as physics, economics, and engineering to optimize processes and make predictions.

4. What are some common mistakes when finding derivatives?

Some common mistakes when finding derivatives include using incorrect notation, forgetting to apply the chain rule or other derivative rules, and making algebraic errors. It is important to double-check your work and practice regularly to avoid these mistakes.

5. Can I use a calculator to find derivatives?

Yes, most scientific calculators have a built-in derivative function that can be used to find derivatives. However, it is important to understand the concepts and rules behind derivatives in order to use the calculator correctly and verify the results.

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