Stupid q, but...
What is the proof that (5)' =0?
I see that the graph has NO SLOPE, but how to proove it arithmetically?
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5 is a constant. The derivative of any constant is 0.
If you want a more rigorous proof:
Or an even more rigorous proof:
Or, as you pointed out to begin with, this is a "linear function" and its derivative is just a constant- its slope. If f(x)= 5, then f(1)= 5 and f(2)= 5. The slope is .