A calculus how do they get there from here question

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A calculus "how do they get there from here" question

I'm trying to understand this step in my physics book:

From this (K is a constant.)

(1) {\frac {{\it dp}}{{\it dy}}}=Kp

To this

(2) {\frac {{\it dp}}{p}}=K{\it dy}

and then to this

(3) \int \!{p}^{-1}{dp}=\int \!K{dy}

How do they get from (1) to (2) How is it that they can break up the notation for the derivative of p with respect to y and treat it like a fraction where dp is divided by dy?
 
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It's a sloppy but handy shorthand. More correctly you get (1/p)*(dp/dy)=K. Now integrate both sides dy and do a change of variable y->p(y) on the left side.
 
kennykroot said:
I'm trying to understand this step in my physics book:

From this (K is a constant.)

(1) {\frac {{\it dp}}{{\it dy}}}=Kp

To this

(2) {\frac {{\it dp}}{p}}=K{\it dy}

and then to this

(3) \int \!{p}^{-1}{dp}=\int \!K{dy}

How do they get from (1) to (2) How is it that they can break up the notation for the derivative of p with respect to y and treat it like a fraction where dp is divided by dy?
Well, my guess would be that they actually completed Calculus I and so had learned about "differentials" as opposed to "derivatives"!
 
Dick,

Thanks very much.

Kenny
 
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