Homework Help: Tricky Derivative! - I need quick help

1. Oct 18, 2005

dekoi

I am faced with the function:
$$f(x)=\frac{e^x(x^2+x+4)+e^{-x}(x^3-1)(x^8+1)}{(e^x+x^2+1)(x^6e^x+2)}$$

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. Oct 18, 2005

whozum

I would break it up and brute force it. I don't see any shortcuts.

3. Oct 18, 2005

dekoi

4. Oct 18, 2005

Tom Mattson

Staff Emeritus
I don't see anything that can be done to make this less painful.

5. Oct 18, 2005

hotvette

You might (??) gain some simplicity by multiplying out all of the polynomials before plug-n-chug......

6. Oct 18, 2005

dekoi

I guess I will have to....

7. Oct 19, 2005