Help finding the derivative of rational/radical functionby jmanna98 Tags: derivative, limit, radical, rational 

#1
Jul1211, 07:23 PM

P: 6

Please help me break down the first couple parts of this derivative question. This question gets a bit ugly:
Find the derivative of F(x)=(1/sqrt(2x)) +2x 



#2
Jul1211, 07:41 PM

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You can rewrite F(x) = 2x  (2x)^(1/2)
Try taking the derivative of this expression. 



#3
Jul1211, 08:21 PM

P: 6

ya but then how do you multiply out (x+deltax)^.5?




#4
Jul1211, 08:37 PM

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Help finding the derivative of rational/radical function
So, do you need to find the derivative by finding the limit: [itex]\displaystyle \lim_{\Delta x \to 0} \frac{F(x+\Delta x)F(x)}{\Delta x}\,?[/itex]
If so, you'll find it handy to rational the numerator. 



#5
Jul1211, 09:24 PM

P: 6

Yes as delta x approaches zero. I know there is goig to be some conjugate or LCD stuff going on but i got stuck




#6
Jul1211, 09:37 PM

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So far you haven't shown any work at all. What have you tried to do and where, exactly, do you have a problem?




#7
Jul1311, 02:28 AM

P: 6

The first thing I did was sub the function into the derivative formula which made a huge mess of a problem to simplify.
[(1/sqrt2(x+deltax)) +2(x+deltax)]  [(1/sqrt2x)+2x] all over deltax. I am a little rusty on working with radicals and tried a few things that ended up in a mess but I am thinking that I should simplify the numerator of this first by finding the LCD of the rational expressions in the numberator of the whole problem. LCD:(sqrt2(x+deltax))(sqrt2x)? Then multiply by the conjugate? I sorta feel on the right track but at the same time I feel that my LCD is incorrect for some reason. 



#8
Jul1311, 10:44 AM

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[(1/sqrt2(x+deltax)) +2(x+deltax)]  [(1/sqrt2x)+2x] all over deltax [tex]\frac{\displaystyle \frac{1}{\sqrt{2(x+\Delta x)}}\left(\frac{1}{\sqrt{2(x)}}+2x\right)}{\Delta x}\quad\to\quad \frac{\displaystyle \frac{1}{\sqrt{2(x+\Delta x)}}\frac{1}{\sqrt{2(x)}}}{\Delta x}+\frac{2(x+\Delta x) 2x}{\Delta x}[/tex] 



#9
Jul1311, 11:01 AM

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Instead of trying to find the limit of all of the parts of F(x) at one time, break F(x) into two pieces: 2x and the radical. Since the derivative of a sum is the sum of the derivatives of the components, you can calculate the two limits and add them together.



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