How to Simplify the Derivative of a Cosine-Sine Product

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Homework Statement



Find the derivative:

F(x)= cos (x)* sin(5x^2 +7)

Homework Equations





The Attempt at a Solution



I used the power rule and the chain rule and wound up with this: but i don't know how to simplify it...

= -sin(x)*sin(5x^2+7)+(10x)*(cos x)*(cos (5x^2+7)
 
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n.a.s.h said:

Homework Statement



Find the derivative:

F(x)= cos (x)* sin(5x^2 +7)

Homework Equations





The Attempt at a Solution



I used the power rule and the chain rule and wound up with this: but i don't know how to simplify it...

= -sin(x)*sin(5x^2+7)+(10x)*(cos x)*(cos (5x^2+7)
You also used the product rule.

I don't see much that you can do to simplify this.
 
n.a.s.h said:

Homework Statement



Find the derivative:

F(x)= cos (x)* sin(5x^2 +7)

Homework Equations





The Attempt at a Solution



I used the power rule and the chain rule and wound up with this: but i don't know how to simplify it...

= -sin(x)*sin(5x^2+7)+(10x)*(cos x)*(cos (5x^2+7)

yeah sorry i meant product rule
 
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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