Differentiation tricks/shortcuts

[Leb]

This is not a specific HW/CW question, just a gap I have and want to fill.
I came from a school in which calculus was only introduced in the last year so I learned only the basics.

Now, I see more and more stuff like taking an expression, say A=B+C and simply making it to a dA=dB+dC. The problem I have is actually understanding why can we simply cancel out the 'with respect to' part ? That is in dA(x)/dx, the dx part.

I think the main question is: When can we treat dA(x)/dx as a fraction rather then an 'operator' (could not come up with a better for d/dx).

Thanks!

 

[genericusrnme]

Because when everything is being nice and friendly you essentially can treat them as single objects.
If you want to rid yourself of confusion define dA = dA/dx then dA=dB+dC is returned to it's former glory.