# 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