(adsbygoogle = window.adsbygoogle || []).push({}); use the definition of the derivative to compute the derivative of the function at x=1

f(x) = 1/(1 + x 2) for all x.

3. The attempt at a solution

i put it into lim[ (f(x)-f(x_{o}))/x-x_{o}] form and got

[(1/1+x^{2}) - (1/2)] <---------numerator

___________________________ <----- division sign ("over")

x-1 <----------- denomenator

form and from there cancelled to

2-1-x^{2}/ 2(x^{2}+1)

and then again to -x^{2}+ 1 / 2(x^{2}+1)

but now im stuck and cant find a cancellation to calculate the limit at x=1 without getting a 0 in there soemwhere

if i stick this into the limit calculation formula itll just give me a 0 and thats no good. i already know the answer is -1/2 but i cant quite get there. any help is appreciated, thanks.

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# Using definition of derivative to calculate, stuck, cant find a cancellation

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