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IsTim
 3 years ago
Use the first principles definition to determine the first derivative of sqrt(2x1)
IsTim
 3 years ago
Use the first principles definition to determine the first derivative of sqrt(2x1)

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IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0This is as far as I got:dw:1340139301477:dw

mashe
 3 years ago
Best ResponseYou've already chosen the best response.0Let's look at the definition: \[\lim_{h \rightarrow a} f(x)=[f(x+h) f(x) ]/h\]

mashe
 3 years ago
Best ResponseYou've already chosen the best response.0Your f(x) = sqrt(2x1), and a=0. So you want to find the limit of f(x) as h approaches 0

mashe
 3 years ago
Best ResponseYou've already chosen the best response.0So you have \[\lim_{h \rightarrow 0} \sqrt(2x1)= \sqrt (2(x+h)1)  \sqrt (2x1)/h\] where h is the denominator and everything else is on top, the numerator

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0As for your latter instructions. I understand, and have reached past that point. The reaffirmation is appreciated.

mashe
 3 years ago
Best ResponseYou've already chosen the best response.0Look at the third picture here: http://www.intmath.com/differentiation/3derivativefirstprinciples.php and the explanation below it states why a=0

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0Ok. I think I understand; The IROC is 0 at a right. Let's continue.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3Where are you at @IsTim ? \[\lim_{h \rightarrow 0}\frac{\sqrt{2(x+h)1}\sqrt{2x1}}{h}\] This is where you at right?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3You need to rationalize the numerator. We are trying to manipulate this problem so that when we plug in 0 for h we don't get 0 on the bottom.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3Think there is something wrong ... because you should be able to get that h canceled

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3\[\lim_{h \rightarrow 0}\frac{\sqrt{2x+2h1}\sqrt{2x1}}{h} \cdot \frac{\sqrt{2x+2h1}+\sqrt{2x1}}{\sqrt{2x+2h1}+\sqrt{2x1}}\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3So that is what you did?

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0Yes, that was my previous step before this.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3\[\lim_{h \rightarrow 0} \frac{(2x+2h1)(2x1)}{h(\sqrt{2x+2h1}+\sqrt{2x1})}\] Is this what you got next?

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0I then cancelled out 2a and 2a.

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0I forgot to cancel 1 and 1.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3So that means we have \[\lim_{h \rightarrow 0}\frac{2h}{h(\sqrt{2x+2h1}+\sqrt{2x1})}\] Correct?

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.3Do you know what to do from here?

IsTim
 3 years ago
Best ResponseYou've already chosen the best response.0Yes. thank you very much.
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