greg1313 wrote:Find dy/dx, then multiply both sides of the equation by dx.
No need to do that. although the thought process is the same. Just write the expression straightaway in terms of differentials, not the derivative ...same result... dy = [expression]dx
That is a good practice [technique] when doing implicit differentiation as well...
3x^2 - 5xy2 + y^3
==> 6xdx - 10xydy -5y^2dx + 3y^2dy = (6x - 5y^2)dx + (3y^2 - 10xy)dy
which can be written as a derivative wrt any other variable, even time ...
==> (6x - 5y^2)[dx/dt] + (3y^2 - 10xy)[dy/dt]
Or , if 3x^2 - 5xy2 + y^3 = 0
(6x - 5y^2)dx + (3y^2 - 10xy)dy = 0
==> dy/dx = ( 5y^2 - 6x)/(3y^2 - 10xy)
Of course, when finding a derivative this way there would be only the one line written down in stages, not the several lines to demonstrate as above. One should never write bits and pieces, but the full expression when finding derivatives that way. Writing only as differentials, as initially, is quite legitimate.