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This leaflet provides a rough and ready introduction to differentiation. This is a technique used to calculate the gradient, or slope, of a graph at different points. The gradient function. Given a function, for example, y = x2, it is possible to derive a formula for the gradient of its graph.
1 Introduction In day to day life we are often interested in the extent to which a change in one quantity affects a change in another related quantity. This is called a rate of change. For example, if you own a motor car you might be interested in how much a change in the amount of fuel used affects how far you have travelled.
Chapter 2. Derivatives (1)15 1. The tangent to a curve15 2. An example { tangent to a parabola16 3. Instantaneous velocity17 4. Rates of change17 5. Examples of rates of change18 6. Exercises18 Chapter 3. Limits and Continuous Functions21 1. Informal de nition of limits21 2. The formal, authoritative, de nition of limit22 3. Exercises25 4 ...
INTRODUCTION TO DIFFERENTIATION. GRADIENT OF A CURVE. We have looked at the process needed for finding the gradient of a curve (or the rate of change of a curve). We have defined the gradient of a curve at a particular point as being the gradient of the tangent to the curve at that point.
Okay, so we know the derivatives of constants, of x, and of x2, and we can use these (together with the linearity of the derivative) to compute derivatives of linear and quadratic functions. To compute the derivatives of all polynomials, we’d need to know the derivatives of xn for higher n. How can we do this? Let’s start with an example: d ...
CHAPTER 1 Introduction to Calculus 1.1 Velocity and Distance 51 1.2 Calculus Without Limits 59 1.3 The Velocity at an Instant 67 1.4 Circular Motion 73 1.5 A Review of Trigonometry 80 1.6 A Thousand Points of Light 85 CHAPTER 2 Derivatives 2.1 The Derivative of a Function 87 2.2 Powers and Polynomials 94 2.3 The Slope and the Tangent Line 102
By Chris Fenwick. Uploaded on 06/02/2024. fenwick_chris@hotmail.com, uczlcfe@ucl.ac.uk. Table of Content. 1.1 Introduction ..................................................................................................................................... 1. 1.2 The derivative as the slope of a curve at a point
