Can we apply u/v rule to dy/dx?

Question

Single derivative of a function y is dy/dx. To find double derivative we write d²y/dx² or d(dy/dx)/dx. So it is correct to write it as [d(dy)dx-d(dx)dy]/(dx)² ?

Answer 1

You are applying the quotient rule to a symbol not a fraction.

There are cases that we consider dy/dx as a fraction.

For example if $$x=x(t)$$ and $$y=y(t)$$ are parametric functions then $$ dy/dx=\frac {dy/dt}{dx/dt}$$