The rules of calculus

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The rules of calculusShairy BalicaoMerced College1How do we find derivatives (in practice)?Differential calculus is a procedure for finding the exact derivative directly from the formulaof the function, without having to use graphical methods. In practise we use a few rules thattell us how to find the derivative of almost any function that we are likely to encounter. In thissection we will introduce these rules to you, show you what they mean and how to use them.Warning! To follow the rest of these notes you will need feel comfortable manipulatingexpressions containing indices. If you find that you need to revise this topic you may find theMathematics Learning Centre publication Exponents and Logarithms helpful.1.1Derivatives of constant functions and powersPerhaps the simplest functions in mathematics are the constant functions and the functions ofthe form xn.Rule 1 If k is a constant thenRule 2 If n is any number then.Rule 1 at least makes sense. The graph of a constant function is a horizontal line and ahorizontal line has slope zero. The derivative measures the slope of the tangent, and so thederivative is zero.How you approach Rule 2 is up to you. You certainly need to know it and be able to use it.However we have given no justification for why Rule 2 works! In fact in these notes we willgive little justification for any of the rules of differentiation that are presented. We will showyou how to apply these rules and what you can do wit … Purchase document to see full attachment

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