What is the significance of the 1/b factor in this differentiation problem?

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The discussion centers on understanding the significance of the 1/b factor in a differentiation problem. Participants question the rationale behind a division by b, noting that it could lead to incorrect units. They clarify that the 1/b factor arises from differentiation and cancels out an earlier b factor present in the equation. The conversation highlights the importance of recognizing how constants affect the differentiation process. Overall, the exchange emphasizes the need for careful attention to factors in mathematical solutions.
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Homework Statement


Screenshot_2015-08-05-16-27-07-1.png

Homework Equations

The Attempt at a Solution


This is actually part of the solution that was provided by the professor. However, I do not fathom two portions of the steps taken (written in orange). Part of the solution is in the picture below.
Screenshot_2015-08-05-16-37-12-1.png


Please help
 
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Why do you expect a division by b? That would get the units wrong.
The added constant could come from a wheel that moves (rolls on the floor). If this is the horizontal component, it does not matter anyway.
 
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Before differentiation there was a factor b. The 1/b that came as a result of the differentiation has canceled that.
 
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haruspex said:
Before differentiation there was a factor b. The 1/b that came as a result of the differentiation has canceled that.
Gosh, I didn't notice that haha
. Thanks
 

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