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If I have the equation

[tex] y' = ax - by [/tex]

where [tex] y = y(t) , x= x(t)[/tex]

and [tex] y' = \frac{dy}{dt} [/tex]

then what is

[tex] \frac {d}{dy} y' = \frac {d}{dy}(ax - by) [/tex]

?

I think it would come out to

[tex] \frac {dy'}{dy} = a \frac {dx}{dt}\frac {dt}{dy} - b [/tex]

Is that right? In general, is y' a function of y or would the first term on the left be 0?

Thanks!

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# Quick chain rule q

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