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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)

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does anyone know how to simplify the equation first before taking it's derivative?
can you rewrite the equation using the equation tool on this site. It is tough to see in this form.

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Other answers:

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

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