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

[shanepitts]

Homework Statement

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.

Please help

 

[mfb]

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.

 

[haruspex]

Before differentiation there was a factor b. The 1/b that came as a result of the differentiation has canceled that.

 

[shanepitts]

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