Could it be impossible to find derivative by basic definition?

Stramonium
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(I am sorry, totally forgot about solving quadratic equations, close the topic please)

Homework Statement



Finding derivative of the equation like F(x) = 5x / (1+x^2) by definition (ƒ(a+h) - f (a))/h is easy (point 2;2), but I got really stuck in finding a way to solve it by basic definition ( f(y) - f(a) )/( x - a ) :(

It seems to me there are much more such equations. Is there any way to do it?
 
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Isn't that the same thing?
As far as I know, the basic definition of derivative is:
23b7112ec7aa5d19157cf84bd3b392e8.png
 
The same, I just had difficulties with canceling equation derived from y - y1 / x - x1, because I totally forgot about solving quadratic equations:( It seemed strange to me on that moment that I could solve the (f(h) - f(a)) / a, but not another form:) Close the topic please.
 
Topics are not closed without a good reason.
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...
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