Introduction to calculus

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An Introduction to CalculusShairy Balicao2016Merced CollegeMerced College, 2016Some rules of differentiation and how to use themDerivatives can be used in economics whenever we want to talk about a rate of change or wantto maximise or minimise something. For example, marginal cost is the rate of change of totalcost with respect to output, so marginal cost can expressed as the derivative of total cost.In the following notes, we will give a few rules so that you can find derivatives of simplepolynomial functions and then discuss how they can be used.Notation We will use y to represent our dependent variable and q as our independent variable,so we will differentiate with respect to q.We may use functional notation and write y = f(q) which means that y is a function of q. So, y= f(q) + g(q) means that y is the sum of two functions of q, one called f(q) and one called g(q).We will express the derivative of y with respect to.dydfIf we use functional notation and write y = f(q) then = . That is, the derivativedqdqof y with respect to q can be written as the derivative of f with respect to q.Some rules of differentiationRule 1. If y = c, where c is an arbitary constant, then.For example, if p = 2000, then.Rule 2. If y = kqn where n is any number and k is a constant, then.For example, if TC = 2q2, then.Rule 3. If y = f(q) + g(q), then.For example, if TC = 12q + 2q2, thenThese are not the only rules for differentiation, but if we consider … Purchase document to see full attachment

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