Break up the fraction into the product of two fractions

Write the x in the denominator as x-1 in the numerator.
 
Use the first principle of derivatives 
 
 

You can keep going by writing the negative exponent of x in
the numerator as a positive exponent of x in the denominator, 
then getting an LCD, etc.

Edwin

I taught calculus for 40 years but never heard of "first principle".  So I
assumed you meant the first derivative formula you learn which is the derivative
of a power of x.  You haven't gotten to the short-cut formulas yet.

What you want is what we called "by using the definition of the derivative" or
"by the limit of the difference quotient".



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Multiply top and bottom by LCD = 2x(x+h)







Factor h out of the numerator:



Cancel h's





As h approaches 0 the numerator and denominator approach what we
get if we substitute 0 for h, so the limit as h approaches 0 is:





Edwin