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
Derivative by first principle refers to using algebra and limits
to find a general expression for the slope of a curve.
It is also known as the delta method.
What Edwin used in his solution, is NOT first principle method.
Taking derivative with the use of table functions IS NOT first principle.
See your Calculus textbook and/or many sources in the Internet, like these
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
