# Thread: Problem simplifying?

1. ## Problem simplifying?

So, I've noticed that I don't have any problems setting up a derivative, but simplifying the quantity after applying the quotient rule, product rule, chain rule, etc. (or even a combination of them) seems to lead to a huge disaster every time. Is there some trick or way that I could avoid these pitfalls? I'm come to realize its holes in my Pre-Algebra and Algebra skills, but I don't have the time to re-teach myself every rule. Any suggestions would be appreciated.

2. Originally Posted by CALsunshine
So, I've noticed that I don't have any problems setting up a derivative, but simplifying the quantity after applying the quotient rule, product rule, chain rule, etc. (or even a combination of them) seems to lead to a huge disaster every time. Is there some trick or way that I could avoid these pitfalls? I'm come to realize its holes in my Pre-Algebra and Algebra skills, but I don't have the time to re-teach myself every rule. Any suggestions would be appreciated.
There is no substitute for practice. You have identified an area where you are weak (its a fairly common one, actually) and you need to buckle down to it.

My best suggestion is to start by writing up a "cheat sheet" of factoring rules, addition of fraction rules, etc. Anything that you are having troubles with. Keep it handy when doing homework problems.

-Dan

3. Originally Posted by CALsunshine
So, I've noticed that I don't have any problems setting up a derivative, but simplifying the quantity after applying the quotient rule, product rule, chain rule, etc. (or even a combination of them) seems to lead to a huge disaster every time. Is there some trick or way that I could avoid these pitfalls? I'm come to realize its holes in my Pre-Algebra and Algebra skills, but I don't have the time to re-teach myself every rule. Any suggestions would be appreciated.
One word, practice. It is the best way to get good at these...also certain tricks are always pull out the lowest exponent term out of polynomials

So once again I would suggest just practicing...

Sometimes its nicer to do this

Instead of doing quotient rule with
$\displaystyle \frac{D[\frac{f(x)}{g(x)}]}{dx}$

Rewrite it as $\displaystyle \frac{D[f(x)\cdot{g(x)^{-1}}]}{dx}$

and apply the chain/product rule

also you can try using a little trick I like to do..which is to apply the inverse operation to both sides and differentiate implicity

For example Let $\displaystyle y=\sqrt[5]{x^3-5x+7}$

If you raise both sides to the fifth power you get

$\displaystyle y^5=x^3-5x+7$

Now differentiating both sides(REMEMBER y is a function of x so you must do it implicity)

$\displaystyle 5y^4y'=3x^2-5\Rightarrow{y'=\frac{3x^2-5}{5y^4}}$

and remembering that $\displaystyle y=\sqrt[5]{x^2-5x+7}$

we see that $\displaystyle y'=\frac{3x^2-5}{4(x^3-5x+7)^{\frac{4}{5}}}$

Not the best example..but it works!

Also look up natural log differenatiation