The power rule and the chains rule

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Homework Statement



How do I know for sure when to use the power rule instead of the chain rule and vice versa?

Homework Equations





The Attempt at a Solution

 
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power rule is used when there are no variables in the raised part (ie. x^2 or 3x^6) but chain rule is used if there are variables in the raised part (ie. d/dx (e^(2x))=e^(2x) * d/dx (2x) = 2e^(2x) Chain rule is used in other situations but this is basically the situation where you would have to decide between chain and power rule as you are asking.
 
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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