An economist estimated that the cost function of a single-product firm is: C(Q)

Question

An economist estimated that the cost function of a single-product firm is: C(Q) = 100 + 20Q + 15Q2 + 10Q3. Based on this information, determine the following: g. The marginal cost when Q = 10. When I looked this up on Chegg, it said that the answer is found in 2 steps. In step 1 a derivative is found. This is what I don't understand. The answer said that: MC (Q)=d C(Q)/dQ then it said: d(100+20Q+15Q2 + 10Q3)/dQ Then this was given: 20+30Q+30Q2 My question is.... how did they get "20+30Q+30Q2 ? Would you explain how this derivative was found in layman's terms in the most simple, step by step way possible?

Explanation / Answer

C(Q) = 100 + 20Q + 15Q2 + 10Q3

MC (Q)=d C(Q)/dQ

Marginal cost is achieved by differentiating Cost with respect to Quantity.

Here we use 2 rules of differentiation; 1) Differebtiaiton of a constant is 0, therefore 100 is missing in MC bacuse it is a constant term as it is not associated with Q.

2) Power rule = d (a.xn) /dx = a.n xn-1 => Power will multiply with the variable and power will decrease by 1 unit.

Apply this to 20Q = 20*1 Q1-1 =>20 because Q raised to power 0 is 1

15Q2 = 15*2Q 2-1 => 30Q

10Q3 = 10*3Q3-1 = > 30Q2

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