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If f(x)=[x+1/x1]3 then f'(2)= ?

 

f(x)=3[x+1/x1]2just not sure what to do after that

 Oct 17, 2017
edited by Guest  Oct 17, 2017
edited by Guest  Oct 17, 2017
 #1
avatar+9488 
+1

Remember...

ddxu3=3u2ddxu

 

So

 f(x)=3[x+1x1]2ddx[x+1x1] f(x)=3[x+1x1]2[ddxx+ddx1xddx1] f(x)=3[x+1x1]2[1x2]

 

To find  f'(2) , plug in  2  for  x .

 

f(2)=3[2+121]2[122] f(2)=3[32]2[114] f(2)=3[94][34] f(2)=8116

 

 

( If   f(x)  is meant to be  [x+1x1]3  then you get a different answer. )

 Oct 18, 2017
 #2
avatar+23254 
+2

If  f(x)  =  [x + 1/x - 1]3,  f(x)  is of the form  f(x) = [g(x)]3, so  f'(x)  =  3[g(x)]2·g'(x)

  f(x)  =  [x + 1/x - 1]3     --->     f'(x)  =  3[x + 1/x - 1]3·[1 - 1/x2]

To find f'(2), replace x with 2 in the above derivative, and simplify.  

 Oct 18, 2017

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