Here are my online notes for my calculus i course that i teach here at lamar university. Basic differentiation differential calculus 2017 edition. You may browse all lessons or browse the lessons by lesson series with the links below. It is one of the two traditional divisions of calculus, the other being integral calculus, the study of the area beneath a curve the primary objects of study in differential calculus are the derivative of a function, related notions such as the differential, and. Both these problems are related to the concept of limit. Calculus i or needing a refresher in some of the early topics in calculus. This a vectorvalued function of two real variables. Functions for calculus chapter 1 linear, quadratic. The derivative of the product y uxvx, where u and v are both functions of x is dy dx u.
Multivariable calculus implicit differentiation examples. Differentiation of functions of a single variable 31 chapter 6. Introduction to differential calculus the university of sydney. You appear to be on a device with a narrow screen width i.
More lessons for calculus math worksheets a series of calculus lectures. To read more, buy study materials of methods of differentiation comprising study notes, revision notes, video lectures, previous year solved questions etc. Also learn how to use all the different derivative rules together in. The only thing id wish to have in calc i is the exponential functions, their inverses logs and their derivatives.
The calculus of scalar valued functions of scalars is just the ordinary calculus. For example, you can have a machine that paints things red. For nonlinear functions, such as, the slope can depend on. Functions for calculus chapter 1 linear, quadratic, polynomial and rational this course is intended to remind you of the functions you will use in calculus. Implicit differentiation allows us to determine the rate of change of values that arent expressed as functions. The booklet functions published by the mathematics learning centre may help you. The derivative of fx c where c is a constant is given by. Differentiation and functions in mathematics online course. Differentiation in calculus definition, formulas, rules. In calculus, the mean value theorem states, roughly.
Rememberyyx here, so productsquotients of x and y will use the productquotient rule and derivatives of y. The chain rule tells us how to find the derivative of a composite function. The derivative of the product y uxvx, where u and v are both functions of x is. Given a function and a point in the domain, the derivative at that point is a way of encoding the smallscale behavior of the function near that point.
Due to the nature of the mathematics on this site it is best views in landscape mode. This is a very condensed and simplified version of basic calculus, which is a prerequisite for many courses in mathematics, statistics, engineering, pharmacy, etc. Listofderivativerules belowisalistofallthederivativeruleswewentoverinclass. Derivatives of trig functions well give the derivatives of the trig functions in this section. In calculus, differentiation is one of the two important concept apart from integration. Also learn how to use all the different derivative rules together in a thoughtful and strategic manner. This is an exceptionally useful rule, as it opens up a whole world of functions and equations. If f and g are two functions such that fgx x for every x in the domain of g, and, gfx x, for every x in the domain of f, then, f and g are inverse functions of each other. The process of finding a derivative is called differentiation. Then the derivative of y with respect to t is the derivative of y with respect to x multiplied by the derivative of x with respect to t dy dt dy dx dx dt. Use the rules of differentiation to differentiate functions without going through the process of first principles.
Note, when applying rules of differentiation always ensure brackets are multiplied out, surds are changed to exponential form and any terms with the variable in the denominator must be rewritten in the form. If p 0, then the graph starts at the origin and continues to rise to infinity. Differential calculus by shanti narayan pdf free download. You should be able to verify all of the formulas easily. Up to now, weve been finding derivatives of functions. In mathematics functions are the idealization of how a varying quantity depends on another quantity, and differentiation allows you to find and show rates of change, the two work handinhand. Ive tried to make these notes as self contained as possible and so all the information needed to read through them is either from an algebra or trig class or contained in other sections of the notes. For example, differentiation is a lesson series for learning all about the derivative of a function. In chapter 3, intuitive idea of limit is introduced. Calculus implicit differentiation solutions, examples. The basic rules of differentiation of functions in calculus are presented along with several examples. Product and quotient rule in this section we will took at differentiating products and quotients of functions. Multivariable calculus implicit differentiation this video points out a few things to remember about implicit differentiation and then find one partial derivative.
This book is a revised and expanded version of the lecture notes for basic calculus and other similar courses o ered by the department of mathematics, university of hong kong, from the. Differential calculus is the study of the definition, properties, and applications of the derivative of a function. Understanding basic calculus graduate school of mathematics. The following is a summary of the derivatives of the trigonometric functions. Let us remind ourselves of how the chain rule works with two dimensional functionals. Calculusdifferentiationdifferentiation defined wikibooks. If you put a dog into this machine, youll get a red. But i understand even for traditional calc books, not all of them contain such content. Suppose the position of an object at time t is given by ft. Vectorvalued functions differentiation practice khan.
Differentiation of explicit algebraic and simple trigonometrical functionssine calculus vol. Applications of differentiation boundless calculus. Pdf produced by some word processors for output purposes only. What does x 2 2x mean it means that, for the function x 2, the slope or rate of change at any point is 2x so when x2 the slope is 2x 4, as shown here or when x5 the slope is 2x 10, and so on. Find a function giving the speed of the object at time t. More lessons on calculus in this lesson, we will learn how implicit differentiation can be used the find the derivatives of equations that are not functions. Rememberyyx here, so productsquotients of x and y will use the productquotient rule and derivatives of y will use the chain rule.
It was developed in the 17th century to study four major classes of scienti. The process of finding the derivative is called differentiation. The portion of calculus arising from the tangent problem is called differential calculus and that arising from. Derivatives of exponential and logarithm functions 204. In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change.
The preceding examples are special cases of power functions, which have the general form y x p, for any real value of p, for x 0. The trick is to differentiate as normal and every time you differentiate a y you tack on a y. Functions which have derivatives are called differentiable. In this case kx 3x2 and gx 7x and so dk dx 6x and dg dx 7. A quantity which may assume an unlimited number of values is called a.
Calculusfunctions wikibooks, open books for an open world. If f and g are two functions such that fgx x for every x in the domain of g, and, gfx x, for every x in the domain of. Take a guided, problemsolving based approach to learning calculus. The definition of slope edit historically, the primary motivation for the study of differentiation was the tangent line problem. Indeed, the theory of functions and calculus can be summarised in outline as the study of the doing and undoing of the processes involved figure 3.
As the commission supports depeds implementation of senior high school shs, it upholds the vision and mission of the k to 12 program, stated in section 2 of republic act 10533, or the enhanced basic. These compilations provide unique perspectives and applications you wont find anywhere else. Implicit differentiation find y if e29 32xy xy y xsin 11. All the numbers we will use in this first semester of calculus are. These functions are studied in multivariable calculus which is usually studied after a one year college level calculus course. If we are given the function y fx, where x is a function of time. Teaching guide for senior high school basic calculus. Solved examples on differentiation study material for. The central concepts of differential calculus the derivative and the differential and the apparatus developed in this connection furnish tools for the study of functions which locally look like linear functions or polynomials, and it is in fact such functions which are of interest, more than other functions, in applications.
Some functions can be described by expressing one variable explicitly in terms of. We will be looking at realvalued functions until studying multivariable calculus. Find materials for this course in the pages linked along the left. Calculus bc parametric equations, polar coordinates, and vectorvalued functions defining and differentiating vectorvalued functions vectorvalued functions differentiation ap calc. Functions and their graphs input x output y if a quantity y always depends on another quantity x in such a way that every value of x corresponds to one and only one value of y, then we say that y is a function of x, written y f x.
In particular, if p 1, then the graph is concave up, such as the parabola y x2. A lesson series is a set of lessons that are naturally grouped together. Accompanying the pdf file of this book is a set of mathematica. These few pages are no substitute for the manual that comes with a calculator. All the tools you need to excel at calculus calculus, vol. This book has been designed to meet the requirements of undergraduate students of ba and bsc courses. It is a method of finding the derivative of a function or instantaneous rate of change in function based on one of its variables. Make your first steps in this vast and rich world with some of the most basic differentiation rules, including the power rule. Also browse for more study materials on mathematics here.
Any of several singlevalued or multivalued functions that are inverses of the. Calculus is the study of differentiation and integration this is indicated by the chinese. Find an equation for the tangent line to fx 3x2 3 at x 4. This course will give you a detailed insight to both functions and differentiation, and how to apply them for solving mathematical problems, and questions. In section 1 we learnt that differential calculus is about finding the rates of. Derivatives of exponential and logarithm functions in this section we will. In this booklet we will not however be concerned with the applications of di.