Question

Which notation is most universal for derivatives? f'(x0) or df/dx?

Answer 1

Newton's f' notation is sometimes more convenient, but Leibniz's dy/dx (or df/dx) opens the door to the powerful world of differential equations, making it the more important version. You need to be familiar with both, and usually it's acceptable to use whichever one fits the current problem.

Answer 2

Thanks!

Answer 3

\[\frac{ dy }{ dx }\] is more convenient when the function is further mathematically manipulated.

Answer 4

dy/dx is more standard notation but y' is also applicable when equations become complex and dirty....there is another dot notation used in time derivatives.....where
dot above y indicates dy/dt which can also be written as y'....
all these notations sometimes makes an equation too complex to understand....because if more derivatives are involved...like a equation involving derivatives over space and time at the same time....like one used in EM-wave propagation in Space time....the wave equation.... then there specifying dy/dx or dy/dt will make the equation more easier to read :)

Answer 5

You really need to be fluent in the several varieties of notation. You will often see the forms mixed, even in the same argument, sometimes in the same equation. d/dx especially when the chain rule or the quotient rule is invoked. You see y' type notation in implicit differentiation but it is limited to situations in which it is clearly understood which is the independent variable. I advise you to alternate notations in exercises to be certain you are able to use all of them.