Good day

In my Microeconomics course, we are handling the 4 imperfect competition models.

Currently we are discussing the Cournot Model, however I am unsure about a certain example. This is given as a lecture example (all information provided).

> 
> Let us first assume that we start with a single firm (monopoly).
> 
> 
> This monopoly is the owner of a costless spring (and sells the water).
> 
> 
> I.e., MC = 0
> 
> 
> Start with our demand function:
> 
> 
> 

```
Q = 120 – P
Now, determine the profit maximizing price/output combination.
MR = MC
MC = 0
Q = 120 – P (Demand function) 
P = -Q + 120
Thus, MR = -2Q + 120
Thus -2Q + 120 = 0
Thus Q = 60
P = 60
Profits = 3600

```

I am familiar with the concept of calculating each firm's demand function, what confuses me is, in this example, we have a a single firm (monopoly) and when deriving its mariginal revenue function, one should end up with the following:

```
P = -Q + 120

```

`d/dQ = P' = -1` (using chainrule for -Q => -1 and dQ of constant = 0)

thus `MR = P' = -1`

but in the example given, we arrive at:

```
MR = -2Q + 120

```

What am I missing or is this example incomplete (not all information given)?