I think rather d/dx is the operator. You apply it to an expression to bind free occurrences of x in that expression. For example, dx²/dx is best understood as d/dx (x²). The notation would be clear if you implement calculus in a program.
My initial thought was that it's surprising that the engineer is using i whereas the mathematician is using j. But I know some engineers who are hardcore in favour of i. No mathematicians who prefer j though. So if such an engineer were dating a mathematician of all people who used j, I could see that being ♠ .