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iop360
Group Title
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)
 2 years ago
 2 years ago
iop360 Group Title
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)
 2 years ago
 2 years ago

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iop360 Group TitleBest ResponseYou've already chosen the best response.1
does anyone know how to simplify the equation first before taking it's derivative?
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.1
can you rewrite the equation using the equation tool on this site. It is tough to see in this form.
 2 years ago

iop360 Group TitleBest ResponseYou've already chosen the best response.1
\[y = \frac{ 7 }{ x^3 }\sqrt{196x^6 + 364x^2 + \frac{ 169 }{ x^2 }}\]
 2 years ago

iop360 Group TitleBest ResponseYou've already chosen the best response.1
Answer is \[\frac{ dy }{ dx } = \frac{ 364 }{ x^5 }\]
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.1
I don't know how to simplify the radical. I would only know how to differentiate right away and it'll get messy
 2 years ago

iop360 Group TitleBest ResponseYou've already chosen the best response.1
ok thanks anyway
 2 years ago

iop360 Group TitleBest ResponseYou've already chosen the best response.1
you would use the product rule right?
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.1
I'm doing it too. it's getting pretty rough
 2 years ago

iop360 Group TitleBest ResponseYou've already chosen the best response.1
\[y' = 21x ^{4} (196x^6 + 364x^2 + 169x^{2})^{1/2} + 7x ^{3}(\frac{ 1 }{ 2 } (196x^6 + 364 + 169x ^{2})^{1/2}(1176x^5 +728x 338x ^{3})^{1/2}\]
 2 years ago

iop360 Group TitleBest ResponseYou've already chosen the best response.1
simplifying is the hardest part
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
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
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
OH! yes found it! :)
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
364 = 2 (13*14)
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
(14x^4 + 13)^2 I think it'll simplify like that.
 2 years ago

iop360 Group TitleBest ResponseYou've already chosen the best response.1
so how would this look like
 2 years ago

iop360 Group TitleBest ResponseYou've already chosen the best response.1
after simplifying?
 2 years ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
dw:1348968835510:dw Hmm, I think it simplifies like this, looks much easier to deal with :) I got lazy on the multiplying there hehe
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.1
I got the same thing. great job finding the factorization pattern @zepdrix
 2 years ago

iop360 Group TitleBest ResponseYou've already chosen the best response.1
how it go from the original to this though
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.1
Ok I'll type this one out
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.1
I'm going to leave off the radical for now ok?
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.1
\[196x ^{6}+363x ^{2}+\frac{ 169 }{ x ^{2} }\]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
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.1
notice that the numerator looks just like a polynomial
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.1
\[\frac{ (14x ^{4}+13)(14x^{4}+13) }{ x ^{2}}\]
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.1
\[\frac{ \sqrt{(14x^{4}+13)^{2}} }{ \sqrt{x^{2}} }\]
 2 years ago

ChmE Group TitleBest ResponseYou've already chosen the best response.1
You probably see it now
 2 years ago
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