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 2 years 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)
 2 years 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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

ChmE
 2 years ago
Best 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

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

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

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