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anonymous
 one year ago
Find the derivative using the quotient rule:
1  (64/x^3)
anonymous
 one year ago
Find the derivative using the quotient rule: 1  (64/x^3)

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geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Really, quotient rule? Well, this rule states that \(\left(\dfrac{f(x)}{g(x)}\right)' = \dfrac{f'(x)~g(x)  f(x)~g'(x)}{(~g(x)~)^2}\) Here, you have \(f(x)=64\) and \(g(x)=x^3\).

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Remember that derivative of constant is zero.

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Denominator is \(x^3\) or \(x^2\)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0These are the steps I did d/dx (1) = 0 \[\frac{ d }{ dx }  \frac{ 64 }{ x ^{3} } =\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{  x ^{3}(0)  (64)3x ^{2} }{ (x ^{3})^{2} }\]

triciaal
 one year ago
Best ResponseYou've already chosen the best response.064 can be written as 4^3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@geerky42 denominator is x^3. Originally I made a mistake in solving the problem; as I'm typing my steps I think I realized my mistake.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ 0 192x ^{2}}{ x ^{6} } =  \frac{ 192 }{ x ^{4} }\]

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Supposed to be \[\frac{ \text x ^{3}(0)  (\color{red}{\textbf}64)3x ^{2} }{ (x ^{3})^{2} }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I do think though it would be easier to solve by rewriting it as \[64\frac{ d }{ dx }\frac{ 1 }{ x ^{3} } =64\frac{ d }{ dx }x ^{3} = \] and using the power rule \[64(3x ^{31}) = 192x ^{4} =  \frac{ 192 }{ x ^{4} }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@geerky42 Thank you for your help

geerky42
 one year ago
Best ResponseYou've already chosen the best response.1Yeah power rule is preferable, but you were asked to use quotient rule lol. Careful with minus sign. Final answer should be \(\dfrac{192}{x^4}\).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@geerky 42 You are correct, the final answer should not have the negative sign.

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437441608527:dw
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