# Mathematical analysis of Marginal Cost

Marginal cost is the cost associated with producing one more unit of output. Mathematically speaking, marginal cost is equal to the change in total cost divided by the change in quantity.

$\ MC(q_{1},q_{2})=\frac{TC(q_{2})-TC(q_{1})}{q_{2}-q_{1}}$

Marginal cost can either be thought of as the cost of producing the last unit of output or the cost of producing the next unit of output. Because of this, it's sometimes helpful to think of marginal cost as the cost associated with going from one quantity of output to another, as shown by q1 and q2 in the equation below.

To get a true reading on marginal cost, q2 should be just one unit larger than q1.

That said, as we consider smaller and smaller changes in quantity, marginal cost converges to the derivative of total cost with respect to quantity.

$\ MC(q_{1},q_{2})=\frac{dTC}{dQ}$

What if we need to calculate marginal cost as we go from one output point to a much bigger one?