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Quotient Rule Derivative Practice

xeuphie

New member
Joined
Nov 28, 2015
Messages
1
So, I've been doing some derivative practice using random worksheets off the internet. I started running into some problems on this worksheet and I'm not quite sure what I'm not understanding. I would be able to solve some problems and then other problems I would be totally off? What am I not seeing?

Differentiate each function with respect to x.

f(x)= 5/(4x^3+4)
y=4x^3-3x^2/(4x^5-4)
etc etc...

I'll start with the first one. So, firstly
f'(x)= (4x^3+4)(0)-(5)(12x^2)/(4x^3+4)^2
=-5(12x^2)/(4x^3+4)^2

And I would assume I just had to multiply everything out (simplify it) and that'd be the end of it?? It looks like they did the chain rule or something because the answer the worksheet gives is

=-15x^2/4x^6+8x^3+4

I'm at a total loss. I'm assuming I'm making similar mistakes with the second problem and all the other ones I can't really solve. Thanks in advance!
 

ksdhart

Full Member
Joined
Aug 1, 2014
Messages
384
Well, your post is a bit confusing to me, and I'm not 100% sure what the original function you're supposed to differentiate is. I think it's this: \(\displaystyle \frac{5}{4x^3-4}\). If that's the case, then what you've done is correct. But you need to use your algebra skills to simply a bit more. You have this form:

\(\displaystyle \frac{-5\left(12x^2\right)}{\left(4x^3-4\right)^2}\)

Multiply out the numerator and denominator:

\(\displaystyle \frac{-60x^2}{16x^6-32x^3+16}\)

Now do you see any common factors you can take out of the denominator? When you do that, what are you left with?
 
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