I am studying differential equations and I have a question about whats in my lecture notes. Here is a link to the lecture notes:

http://sdrv.ms/1gYECTo

a)

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b)

In the first equation above a) I am trying to get a handle on what is meant by having "d/dx" and "x" on the same side of the equation. I know that the derivative of "x" is "1" by the power rule. So then could the first equation above a) not reduce to:

or is something different meant by the use of "d/dx"?

Thanks for any responses...