Introduction to differential calculus

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Introduction toDifferential CalculusShairy BalicaoMerced CollegeContents1 Introduction1.11.21An example of a rate of change: velocity . . . . . . . . . . . . . . . . . . . 11.1.1Constant velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . .11.1.2Non-constant velocity . . . . . . . . . . . . . . . . . . . . . . . . . .3Other rates of change………………………..42 What is the derivative? 62.1Tangents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2.2The derivative: the slope of a tangent to a graph . . . . . . . . . . . . . .673 How do we find derivatives (in practice)? 93.1Derivatives of constant functions and powers . . . . . . . . . . . . . . . . .93.2Adding, subtracting, and multiplying by a constant . . . . . . . . . . . . .123.3The product rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3.4The Quotient Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.5The composite function rule (also known as the chain rule) . . . . . . . . . 153.6Derivatives of exponential and logarithmic functions . . . . . . . . . . . . .3.7Derivatives of trigonometric functions . . . . . . . . . . . . . . . . . . . . . 2113184 What is differential calculus used for? 244.1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4.2Optimisation problems . . . . . . . . . . . . . . . . . . . . . . . . . … Purchase document to see full attachment

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