Technological University of the Philippines Visayas
computer
MATH 036

Summer 2015
CALCULUS I
Derivatives
Paul Dawkins
Calculus I
Table of Contents
Preface . ii
Derivatives. 3
Introduction . 3
The Definition of the Derivative . 5
Interpretations of the Derivative .11
Differentiation Formulas .20
Product and Quotient Rule
Technological University of the Philippines Visayas
computer
MATH 036

Fall 2015
Republic of the Philippines
TECHNOLOGICAL UNIVERSITY OF THE PHILIPPINES CAVITE CAMPUS
Carlos Q. Trinidad Ave. Salawag, City of Dasmarias, Cavite
ASSOCIATION OF COMPUTER TECHNOLOGY STUDENTS
OFFICERS
S.Y. 20162017
Maita F. Limbo
President
November 11, 2016
Technological University of the Philippines Visayas
computer
MATH 036

Summer 2015
Basic Concepts
of Integration
14.1
Introduction
When a function f (x) is known we can dierentiate it to obtain its derivative df . The reverse
dx
process is to obtain the function f (x) from knowledge of its derivative. This process is called
integration.
Technological University of the Philippines Visayas
computer
MATH 036

Summer 2015
CALCULUS I
Assignment Problems
Derivatives
Paul Dawkins
Calculus I
Table of Contents
Preface. 1
Derivatives . 1
Introduction . 1
The Definition of the Derivative . 2
Interpretations of the Derivative. 4
Differentiation Formulas. 8
Product and
Technological University of the Philippines Visayas
computer
MATH 036

Summer 2015
CALCULUS I
Practice Problems
Derivatives
Paul Dawkins
Calculus I
Table of Contents
Preface . 1
Derivatives. 2
Introduction . 2
The Definition of the Derivative . 3
Interpretations of the Derivative . 3
Differentiation Formulas . 6
Product and Quot
Technological University of the Philippines Visayas
computer
MATH 036

Summer 2015
CALCULUS I
Solutions to Practice Problems
Derivatives
Paul Dawkins
Calculus I
Table of Contents
Preface . 1
Derivatives. 1
The Definition of the Derivative . 2
Interpretations of the Derivative .10
Differentiation Formulas .27
Product and Quotient Rule .4
Technological University of the Philippines Visayas
computer
MATH 036

Summer 2015
CALCULUS I
Practice Problems
Limits
Paul Dawkins
Calculus I
Table of Contents
Preface. 1
Limits . 2
Introduction . 2
Rates of Change and Tangent Lines . 3
The Limit . 5
OneSided Limits. 7
Technological University of the Philippines Visayas
computer
MATH 036

Summer 2015
CALCULUS I
Solutions to Practice Problems
Limits
Paul Dawkins
Calculus I
Table of Contents
Preface . 2
Limits . 2
Rates of Change and Tangent Lines. 2
The Limit .12
OneSided Limits .20
Limit Properties .
Technological University of the Philippines Visayas
computer
MATH 036

Summer 2015
CALCULUS I
Limits
Paul Dawkins
Calculus I
Table of Contents
Preface . ii
Limits . 2
Introduction . 3
Rates of Change and Tangent Lines . 4
The Limit .13
OneSided Limits .23
Limit Propertie