What is the derivative of y=6/x using the first principle?

We have.....

  lim          [ 6/(x+h) - 6/(x) ]   / h    =      

(h→0)

6*lim          [ 1/(x+h) - 1/(x) ]   / h    =    

   (h→0)

6* lim  [ (x) - (x+h)] / [(h)*(x)*(x + h)]  =

    (h→0)

6 * lim [-h] / [(h)*(x)*(x + h)]   =

     (h→0)

-6 * lim [ 1 / ( x² + xh) ]  =

      (h→0)

Now, let (h→0) and we have......

-6/x²   or    -6x^-2

Yet again, look at

http://web2.0calc.com/questions/what-is-the-derivative-of-y-3-sqrt-2x-1-using-the-first-principle

http://web2.0calc.com/questions/what-is-the-derivative-of-y-4sqrt-x-using-the-first-principle

If you have any difficulty after looking at these, ask again.