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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)
 one year ago
 one year ago
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)
 one year ago
 one year ago

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iop360Best ResponseYou've already chosen the best response.1
does anyone know how to simplify the equation first before taking it's derivative?
 one year ago

ChmEBest 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.
 one year ago

iop360Best ResponseYou've already chosen the best response.1
\[y = \frac{ 7 }{ x^3 }\sqrt{196x^6 + 364x^2 + \frac{ 169 }{ x^2 }}\]
 one year ago

iop360Best ResponseYou've already chosen the best response.1
Answer is \[\frac{ dy }{ dx } = \frac{ 364 }{ x^5 }\]
 one year ago

ChmEBest 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
 one year ago

iop360Best ResponseYou've already chosen the best response.1
you would use the product rule right?
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
I'm doing it too. it's getting pretty rough
 one year ago

iop360Best ResponseYou've already chosen the best response.1
\[y' = 21x ^{4} (196x^6 + 364x^2 + 169x^{2})^{1/2} + 7x ^{3}(\frac{ 1 }{ 2 } (196x^6 + 364 + 169x ^{2})^{1/2}(1176x^5 +728x 338x ^{3})^{1/2}\]
 one year ago

iop360Best ResponseYou've already chosen the best response.1
simplifying is the hardest part
 one year ago

zepdrixBest 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
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
(14x^4 + 13)^2 I think it'll simplify like that.
 one year ago

iop360Best ResponseYou've already chosen the best response.1
so how would this look like
 one year ago

zepdrixBest 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
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
I got the same thing. great job finding the factorization pattern @zepdrix
 one year ago

iop360Best ResponseYou've already chosen the best response.1
how it go from the original to this though
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
Ok I'll type this one out
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
I'm going to leave off the radical for now ok?
 one year ago

ChmEBest 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
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
notice that the numerator looks just like a polynomial
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
\[\frac{ (14x ^{4}+13)(14x^{4}+13) }{ x ^{2}}\]
 one year ago

ChmEBest ResponseYou've already chosen the best response.1
\[\frac{ \sqrt{(14x^{4}+13)^{2}} }{ \sqrt{x^{2}} }\]
 one year ago
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