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13.07.2001 · MEEN 364 Parasuram July 13, 2001 1 HANDOUT M.2 - DIFFERENTIATION AND INTEGRATION Section 1: Differentiation Definition of derivative A derivative f ′(x)of a function f(x) depicts how the function f(x) is changing at the point‘x’.

Basic Differentiation - A Refresher 1 Contents Foreword 2 Preliminary work 2 How to use this booklet 2 Reminders 3 Introduction 4 1. Differentiation of a simple power 5 2. Differentiation of a unit power 6 3. Differentiation of a constant 7 4. Differentiation of a simple power multiplied by a constant 8 Notes page 9 5.

A: TABLE OF BASIC DERIVATIVES Let u = u(x) be a differentiable function of the independent variable x, that is u(x) exists. (A) The Power Rule : Examples : d dx {un} = nu n−1. u ddx {(x3 + 4x + 1)3/4} = 34 (x3 + 4x + 1)−1/4.(3x2 + 4)d dx {u} = 12 u.u d dx { 2 − 4x2 + 7x5} = 1 2 2 − 4x2 + 7x5 (−8x + 35x4) d dx {c} = 0 , c is a constant ddx {6} = 0 , since ≅ 3.14 is a constant.

A quotient cannot be differentiated term by term, so it must be rewritten as 2 2 2 4 1 x x x Both terms can now be differentiated to give f (x) = 3 2 2 x x . Note that 2 2 1 x x and differentiation gives 3 3 2 2 x . (Again, there is a quotient rule for differentiation, but we will not study it until Core 3)

In Chapters 4 and 5, basic concepts and applications of differentiation are discussed. ... Accompanying the pdf file of this book is a set of Mathematica.

2.00 4.00 6.00 8.00 100 200 300 (metres) Distance time (seconds) Mathematics Learning Centre, University of Sydney 1 1 Introduction In day to day life we are often interested in the extent to which a change in one quantity

DIFFERENTIATION . Created by T. Madas Created by T. Madas Question 1 Evaluate the following. a) d (5x6) dx d ( )5 30x x6 5 dx = b) 3 2 2 d x dx ...

1. Basic Derivative formulae (xn)0 = nxn−1 (ax)0 = ax lna (ex)0 = ex (log a x) 0 = 1 xlna (lnx)0 = 1 x (sinx)0 = cosx (cosx)0 = −sinx (tanx)0 = sec2 x (cotx)0 = −csc2 x (secx)0 = secxtanx (cscx)0 = −cscxcotx (sin−1 x)0 = 1 √ 1−x2 (cos−1 x)0 = −1 √ 1−x2 (tan−1 x)0 = 1 1+x2 (cot−1 x)0 = −1 1+x2 (sec−1 x)0 = 1 x √ ...

The derivative of f at x = a is the slope, m, of the function f at the point x = a (if ... The following is a table of derivatives of some basic functions:.

Regrettably mathematical and statistical content in PDF files is unlikely to be ... 2 Finding derivatives of simple functions.

Created by T. Madas Created by T. Madas Question 3 Differentiate the following expressions with respect to x a) y x x= −2 64 2 24 5 dy x x dx = − b) 3 y x x= −5 63 2 1 dy 15 9x x2 2 dx = −

1. Basic Derivative formulae (xn)0 = nxn−1 (ax)0 = ax lna (ex)0 = ex (log a x) 0 = 1 xlna (lnx)0 = 1 x (sinx)0 = cosx (cosx)0 = −sinx (tanx)0 = sec2 x (cotx)0 = −csc2 x (secx)0 = secxtanx (cscx)0 = −cscxcotx (sin−1 x)0 = 1 √ 1−x2 (cos−1 x)0 = −1 √ 1−x2 (tan−1 x)0 = 1 1+x2 (cot−1 x)0 = −1 1+x2 (sec−1 x)0 = 1 x √ x2 −1 (csc−1 x)0 = −1 x √ x2 −1 2 ...

Differentiation Formulas d dx k = 0. (1) d dx. [f(x) ± g(x)] = f (x) ± g (x). (2) d dx. [k · f(x)] = k · f (x). (3) d dx. [f(x)g(x)] = f(x)g (x) + g(x)f (x) ...

We collect these formulas in the following table. Rules for Derivatives of Basic Functions function derivative mx + b m xr rxr−1.

DIFFERENTIATION: BASIC CONCEPTS The rate of change is greater in magnitude in the period following the burst of blood. (b) Writing exercise – answers will vary. 36. (a) → → + −−− = == 0 0 (3( ) 2) (3 2) '( ) lim 3 lim 3 h h xh x fx h h h (b) At x =−1, y =3( 1) 2 5−−=−and (1, 5)−− is a point on the tangent line.

Differentiation is all about measuring change! Measuring change in a linear function: y = a + bx a = intercept b = constant slope i.e. the impact of a unit.

A: TABLE OF BASIC DERIVATIVES Let u = u(x) be a differentiable function of the independent variable x, that is u(x) exists. (A) The Power Rule : Examples : d dx {un} = nu n−1. u d dx {(x3 + 4x + 1)3/4} = 3 4 (x3 + 4x + 1)−1/4.(3x2 + 4) d dx {u} = 1 2 u.u d dx { 2 − 4x2 + 7x5} = 1 2 2 − 4x2 + 7x5 (−8x + 35x4) d dx {c} = 0 , c is a ...

DIFFERENTIATION TUTORIAL 1 - BASIC DIFFERENTIATION This tutorial is essential pre-requisite material for anyone studying mechanical engineering. This tutorial uses the principle of learning by example. The approach is practical rather than purely mathematical and may be too simple for those who prefer pure maths.

derivative of a function, for there are various rules of differentiation that ... derivative of the product of two functions is not the simple product of ...

Differentiation Formulas d dx k = 0 (1) d dx [f(x)±g(x)] = f0(x)±g0(x) (2) d dx [k ·f(x)] = k ·f0(x) (3) d dx [f(x)g(x)] = f(x)g0(x)+g(x)f0(x) (4) d dx f(x) g(x ...

arises in many areas of mathematics. You will learn how to use a table of derivatives to obtain the derivative of simple combinations of functions.

Basics of Derivatives Free SEBI e-book c. An options contract binds one party whereas it lets the other party decide at a later date i.e. at the expiration of the option. So, one party has the obligation to buy or sell at a later date whereas the other party can …

Question 1 (non calculator). For each of the following curves find an equation of the tangent to the curve at the point whose x coordinate is given.

Basic Differentiation - A Refresher 7 3. Differentiation of a constant To differentiate s = a where a is a constant. Example • An isolated constant always differentiates to zero. s = 4 Answer ds dt = 0 ds dt = 0 Practice: In the space provided write down the requested derivative for each of the following expressions. (a) s = 5, ds dt (b ...

Differentiation and integration are basic mathematical operations with a wide range of applications in many areas of science. It is therefore important to have good methods to compute and manipulate derivatives and integrals. You proba-bly learnt the basic rules of differentiation and integration in school — symbolic

Derivatives of basic functions. 3.2. Derivative of a sum of functions. 3.3. Derivative of a constant multiple of a function.