endobj (3 Higher Order Partial Derivatives) 21 0 obj x�3PHW0Pp�2� << /S /GoTo /D (section*.1) >> �Rك������uD? /Subtype /Form 36 0 obj << You proba-bly learnt the basic rules of differentiation … endobj It is therefore important to have good methods to compute and manipulate derivatives and integrals. (Table of Contents) 1 0 obj

<< /S /GoTo /D (section*.2) >> << /S /GoTo /D (section.2) >> /Subtype /Form << /S /GoTo /D (section.3) >> <> INTRODUCTION TO DIFFERENTIAL AND INTEGRAL CALCULUS (EXCLUDING TRIGONOMETRIC FUNCTIONS) (A) DIFFERENTIAL CALCULUS 8.A.1 INTRODUCTION Differentiation is one of the most important fundamental operations in calculus. _3��%@ 8 Basic Diﬀerentiation - A Refresher 4. /Matrix [1 0 0 1 0 0] %PDF-1.7 stream >> 10 Algebra of Derivatives: Rules for Computing Derivatives of Various Combinations of Differentiable Functions 275 10.1 Introduction 275 10.2 Recalling the Operator of Differentiation 277 10.3 The Derivative of a Composite Function 290 10.4 Usefulness of Trigonometric Identities in Computing Derivatives 300 10.5 Derivatives of Inverse Functions 302 endobj 39 0 obj << �Mp"� BE/�VV8_�"�(A�(�գ�L�Qt���5�� ϑ�{�obFKԿ\$@�P"�j (2 The Rules of Partial Differentiation) endobj Partial Diﬀerentiation (Introduction) 2. endobj endobj 1.1 Introduction Successive Differentiation is the process of differentiating a given function successively times and the results of such differentiation are called successive derivatives. << /S /GoTo /D (section.1) >> 9 0 obj << /S /GoTo /D (section.4) >>

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those very past An Introduction to Derivatives 1997 0030222834, 9780030222832 Civil procedure , Jack H. Friedenthal, Mary Kay Kane, Arthur Raphael Miller, 1985, Law, 876 pages. The Rules of Partial Diﬀerentiation 3. s = 3t4 • Reduce the old power by one and use this as the new power. ( Solutions to Quizzes) Quiz on Partial Derivatives Solutions to Exercises Solutions to Quizzes The full range of these packages and some instructions, should they be required, can be obtained from our web page Mathematics Support Materials. endobj

Contents . Carol Ann Tomlinson and Marcia Imbeau present these in Leading and Managing a Differentiated Classroom (2010): Misunderstanding Reality Differentiation is a set of instructional strategies. /Type /XObject %PDF-1.7 4 0 obj %PDF-1.4 endobj • understand that differentiation (differential calculus) is used to calculate instantaneous rates of change understand how to apply differentiation to calculate instantaneous rates of

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<< /S /GoTo /D (toc.1) >> 3 0 obj >> endobj Differentiation and integration are basic mathematical operations with a wide range of applications in many areas of science. stream ���\{�'�D��[�@-��3;��1L�J?�[n�Eˈ0C���A؏t�T��.a&\è4%޻D��'�~H�J�"��h�粎�Ar�>�K,a7rJ*eW�T��e�h�5�j� R�� �)֔H��:H�ٖ(ڥ� e�%�G\�f�k5 ��;��� H9����*>`T�u2%hW�\�O���!�b?�I�O�����]�qPx)�4��. • Findthelengthofacurve,theareaofaregion,andthevolumeofasolid. 28 0 obj �,ν��0��Ȼ{? endobj x��ksܸ���+��w�ڊ\$�ٙNǯ4��Mj������Z�}���J����AJ"An�Ns�/;�H D�x ���d��������~�����3|��Nn��o"/�� �y7���U�"�{a������9�� 2 0 obj <> stream (i) f( ) 2 1xx f ( ) 2cx (ii) f( ) 5x x x 3 f( ) 3 5c xx 2 (iii) 3 3 1 f( )xx x 4 4 3 f ( ) 3xx x c (iv) 1 f( )x x x3 3 2 1 3 f ( )xx 3 c (v) 12 2 23 f( ) 2 3x x x xx 2623 23 23 f ( ) 2 3 2 26 x x x xx xx c u u (vi) 11 22 3 f( ) … Differentiation is a philosophy—a way of thinking about teaching and learning.

24 0 obj endobj �P4h0�R�P�Q��[y����\����]-� ����\�o0�;�. 25 0 obj 35 0 obj << /Matrix [1 0 0 1 0 0] It was developed in the 17th century to study four major classes of scientiﬁc and mathematical problems of the time: • Find the tangent line to a curve at a point. � g��JFN��B�Y���� J�D5K���0z�?��:�S����A��|�8��D 32 0 obj

17 0 obj (1 Partial Differentiation \(Introduction\)) Section 1: Introduction to differentiation Solutions to Exercise 1. The higher order differential coefficients are of utmost importance in scientific and engineering applications. >> Higher Order Partial Derivatives 4. �K���;\$�=��f����q�����A��� � ^���X�P�O��jU�լ��/M�[���f.�=��o��=H�K/��O���8?����d��|́��l�c4�����ON�}h��}L����O�w�m?����7T\$ ���% endobj 8 0 obj Example • Bring the existing power down and use it to multiply. ���'��F�L|Z��O�B�0izA*>=���_~�hm}���w�������_߿����^�g���q���_���:O2��LE�/���%��G�˕D�F��5N�d槑b��ML�9-|�Iz�,��YJ?�H�&ɳ�8K���k�� Kp/�������VJ�����5}���_HT�:��G��c�Fq��I�%�P <>/ExtGState<>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/Annots[ 16 0 R] /MediaBox[ 0 0 595.32 841.92] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> /Resources 40 0 R endobj 35 0 obj

<> 1. ^�D���i�e=&��G�T����@!�8 ����r������1�_~_&.NỔ�2:�o&�|K�� �K��\��S�>�-a����B��ar����Jx��K�0h�o\$?q��)Ǎ8�E ߏ�a/�p}; ���k��S�-�^�0�(�{|�!%j@?s{���+d�_od��hp.�(x�Mk

{7�N�Y�����sǛ#d/��?΃8ʀ����X_�2����8�(k�x�=�a ��>v��.��*�|�-��y���q��zO�R���7�����3�\z�59l\$y�:8����?���E��l�vp� ��g�>�i��ya�K�N�z���x}ͮ� �^8�a�y^di�Kl>��C^��?»�N���5|��N�`��J9ƌ���1��4�6� 1�;�� @*��\��Mk��3���E>�@������ �W�O���'zO�Y�!�(ў��;W0�9�� Its theory primarily depends on the idea of limit and continuity of function. << /Type /Page /Parent 1 0 R /LastModified (D:20100603053403+00'00') /Resources 2 0 R /MediaBox [0.000000 0.000000 595.276000 841.890000] /CropBox [0.000000 0.000000 595.276000 841.890000] /BleedBox [0.000000 0.000000 595.276000 841.890000] /TrimBox [0.000000 0.000000 595.276000 841.890000] /ArtBox [0.000000 0.000000 595.276000 841.890000] /Contents 36 0 R /Rotate 0 /Group << /Type /Group /S /Transparency /CS /DeviceRGB >> /Annots [ 6 0 R 7 0 R 8 0 R 9 0 R 10 0 R ] /PZ 1 >> endobj 1 1 Introduction to Differentiation RC 1 2 Finding the Derivative RC 2 3 Differentiating with Respect to Other Variables RC 6 4 Rates of Change RC 7 5 Equations of Tangents RC 8 6 Increasing and Decreasing Curves RC 12 7 Stationary Points RC 13 8 Determining the Nature of Stationary Points RC 14 �\���D!9��)�K���T�R���X!\$ (��I�֨֌ ��r ��4ֳ40�� j7�� �N�endstream stream }ώ��w�Q�~��0���;�b ۲5�{V���-���)�U�ܜ=�>� �5;�d!+��و�%��� 6ut����t�f0� /Filter /FlateDecode ( Solutions to Exercises) /BBox [0 0 3.905 7.054] 36 0 obj <>/Metadata 293 0 R/ViewerPreferences 294 0 R>> z~�b�G�cA�1��D�{i�W���i�����M>�fu1go;�rV������о����UE`�1����

misunderstandings about what differentiation is and isn’t.

endobj /FormType 1 Differentiation: Information Introduction The SEND ode of Practice (2015) makes it clear that differentiation is an expectation: High quality teaching that is differentiated and personalised will meet the individual needs of the majority of children and young people (para. endobj /FormType 1 ��E�5E����Z��&�\$p'��|� |� /Length 78 xڥ�M�0���=n��d��� *̓����EtA�e*�i�҄. This hornbook 5 0 obj endobj Differentiation . 4 *sv jyrgxmsrw sr xli tivmshmg mrxivzep [i lezi xli *syvmiv vitviwirxexmsr f ()= k= fˆ k 2 bk -xwhivmzexmzimw jsvqepp] sfzmsyw f k= bkfˆ k 2 bk ;lir hsiw xlmw gsrzivki#;lirizivfˆ endobj Differentiation . 1.1 Introduction Calculus is the mathematical tool used to analyze changes in physical quantities. /ProcSet [ /PDF /Text ] x��\[o�ʵ~��0�ҁMsH/���V���A��>��)��,)\$����.s!Er;��4�c��Ykf��[���eՔ�|و��˦ɗŝ���j�4���}��+���ߗ��)���_�� ^��n����W��_cq_����;���_ƱP��JN�q��R����|ˏ���{n������?b�E��8��i��J���A�%0f��a��%�t��1�/����x�N\� �1������K��ٕp������L#�e��

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