My economics textbook said that the total revenue formula for a monopoly is 80q

Question

My economics textbook said that the total revenue formula for a monopoly is
80q - (2*(qsquared))

It said we can therefore derive that the formula for marginal revenue is

80 - 4q

I don't understand this. If they're dividing both parts by q, the answer should be
80 - 2q.

(Just to show that my math is correct, let's suppose that the value of q is 3. The value of (2*(qsquared)) would be 2 * 9, or 18. If we then divide that by 3, we get 6, or 2 q.)

Another book says:

TR = 50q - qsquared, and therefore MR = 50 - 2q.
Here again, I don't understand the math.

Thank you

Explanation / Answer

You need a quickie course in elementary calculus (taking derivatives). Marginal revenue is calculated by taking the derivative of the total revenue function. The formula for the derivative of a power (x^n) is nx^(n-1). So if the revenue function is 80q- 2q^2 The marginal revenue function is 1*80*q^(1-1) -2*2q^(2-1) 80- 4q.

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