anonymous
  • anonymous
Let y = (7/x^3)(√196x^6 +364x^2 + (169/x^2)) Find the derivative of y. Hint: Simplify y before computing the derivative. Answer: (-364/x^5)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
does anyone know how to simplify the equation first before taking it's derivative?
anonymous
  • anonymous
can you rewrite the equation using the equation tool on this site. It is tough to see in this form.
anonymous
  • anonymous
yep

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More answers

anonymous
  • anonymous
\[y = \frac{ 7 }{ x^3 }\sqrt{196x^6 + 364x^2 + \frac{ 169 }{ x^2 }}\]
anonymous
  • anonymous
Answer is \[\frac{ dy }{ dx } = \frac{ -364 }{ x^5 }\]
anonymous
  • anonymous
I don't know how to simplify the radical. I would only know how to differentiate right away and it'll get messy
anonymous
  • anonymous
ok thanks anyway
anonymous
  • anonymous
you would use the product rule right?
anonymous
  • anonymous
ya.
anonymous
  • anonymous
I'm doing it too. it's getting pretty rough
anonymous
  • anonymous
\[y' = -21x ^{-4} (196x^6 + 364x^2 + 169x^{-2})^{1/2} + 7x ^{-3}(\frac{ 1 }{ 2 } (196x^6 + 364 + 169x ^{-2})^{-1/2}(1176x^5 +728x -338x ^{-3})^{-1/2}\]
anonymous
  • anonymous
whoops lol
anonymous
  • anonymous
simplifying is the hardest part
zepdrix
  • zepdrix
Hmm there is something going on inside this square root, I'm trying to figure it out. Not quite there yet, but I think it's not long off. 196 = 14^2 169=13^2 Hmmmm
zepdrix
  • zepdrix
OH! yes found it! :)
zepdrix
  • zepdrix
364 = 2 (13*14)
zepdrix
  • zepdrix
(14x^4 + 13)^2 I think it'll simplify like that.
anonymous
  • anonymous
nice
anonymous
  • anonymous
so how would this look like
anonymous
  • anonymous
after simplifying?
zepdrix
  • zepdrix
|dw:1348968835510:dw| Hmm, I think it simplifies like this, looks much easier to deal with :) I got lazy on the multiplying there hehe
anonymous
  • anonymous
thanks
anonymous
  • anonymous
I got the same thing. great job finding the factorization pattern @zepdrix
anonymous
  • anonymous
how it go from the original to this though
anonymous
  • anonymous
Ok I'll type this one out
anonymous
  • anonymous
I'm going to leave off the radical for now ok?
anonymous
  • anonymous
k
anonymous
  • anonymous
\[196x ^{6}+363x ^{2}+\frac{ 169 }{ x ^{2} }\]Find a common denominator and add\[\frac{ 196x ^{8}+364x ^{4}+169 }{ x ^{2} }\]rewrite the constants\[\frac{ 14*14x ^{8}+2*14*13x ^{4}+13*13 }{ x ^{2} }\]You still with me so far
anonymous
  • anonymous
notice that the numerator looks just like a polynomial
anonymous
  • anonymous
yep
anonymous
  • anonymous
\[\frac{ (14x ^{4}+13)(14x^{4}+13) }{ x ^{2}}\]
anonymous
  • anonymous
oh alright
anonymous
  • anonymous
\[\frac{ \sqrt{(14x^{4}+13)^{2}} }{ \sqrt{x^{2}} }\]
anonymous
  • anonymous
You probably see it now
anonymous
  • anonymous
thanks!

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