Q:

Does differentiation symbol need parentheses or?

Suppose I have this expression:
$$\frac{d}{dx}(e^{x})^2 + 6$$
Does it mean to differentiate $6$ too or just the first term?

This is an exercise on a calculus course that I'm doing on Coursera.
Unfortunately anything printed has a weight greater than the onlooker's intelligence. It's beyond me how people on the course forum including the two professors who happen to be doctors can't understand the basic and obvious meaning of parentheses.

A:

Short of the possibility that you are reading someone else's bad writing,
$$\frac{d}{dx}(e^x)^2+6 = 2e^{2x}+6 \neq \frac{d}{dx}\left((e^x)^2+6\right) = 2e^{2x}.$$
Mathematical notation is supposed to be quite unambiguous, and so I would not differentiate the constant unless I knew that the author was just being sloppy and really intended the latter.
The differential operator $\frac{d}{dx}$ distributes over addition just like scalar multiplication, and so these parentheses are quite necessary if it is the author's intention to differentiate the 6.

