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Differentiation 8 examples using the quotient rule

concise derivation of differentiation from first principles •The aim now is to give a number of examples •Here the focus is on the quotient rule in combination with a table of results for simple functions Slides by Anthony Rossiter 2 ( ) ( ) v x u x y v 2 dx dv u dx du v dx dy



Differential Equations I

are all examples of boundary conditions Boundary-value problems, like the one in the example, where the boundary condition consists of specifying the value of the solution at some point are also called initial-value problems (IVP) Example 1 5 An analogy from algebra is the equation y = √ y +2 (1 1)



Calculus Cheat Sheet - Lamar University

Calculus Cheat Sheet Visit http://tutorial math lamar edu for a complete set of Calculus notes © 2005 Paul Dawkins Derivatives Definition and Notation If yfx then



nn) (cx ncx nn) - Lamar University

Common Derivatives and Integrals Visit http://tutorial math lamar edu for a complete set of Calculus I & II notes © 2005 Paul Dawkins Inverse Trig Functions 1



Definition of derivative

Contents •1 Slope-The Concept •2 Slope of a curve •3 Derivative-The Concept •4 Illustration of Example •5 Definition of Derivative



Arithmetic Analogues of Derivations

p-derivation if and only if the map x ‹ xq q pdxis a ring homomor-phism Remark IfAhas no nontrivial idempotents and p is a nonzero divisor then all operators d considered in the foregoing examples are jet opera-tors Indeed for any such d one trivially checks that d 0 s d 1 s 0 On



DIFFERENTIATING UNDER THE INTEGRAL SIGN

We will apply (1 2) to many examples of integrals, in Section12we will discuss the justi cation of this method in our examples, and then we’ll give some more examples 2 Euler’s factorial integral in a new light For integers n 0, Euler’s integral formula for n is (2 1) Z 1 0 xne xdx= n;



MATH 221 FIRST SEMESTER CALCULUS

9 Examples { functions with and without maxima or minima71 10 General method for sketching the graph of a function72 11 Convexity, Concavity and the Second Derivative74 12 Proofs of some of the theorems75 13 Exercises76 14 Optimization Problems77 15 Exercises78 Chapter 6 Exponentials and Logarithms (naturally)81 1 Exponents81 2

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