I am faced with the function:(adsbygoogle = window.adsbygoogle || []).push({});

[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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# Homework Help: Tricky Derivative! - I need quick help

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