0000009055 00000 n 0000044380 00000 n The basic rules of Differentiation of functions in calculus are presented along with several examples . << � �����Y�H���?�`��'P(��e�@!���@����cXbx��g���� M�Ļ(c��$�� �/E��.d �x��ƕǼ%�w1p�iF �g������3� H��� endstream endobj 642 0 obj <> endobj 643 0 obj <> endobj 644 0 obj <>stream �8���^����r���P�� H�\�_k�@��|�ylJ4s�� 0000002791 00000 n �MFk����� t,:��.FW������8���c�1�L&���ӎ9�ƌa��X�:�� �r�bl1� PART A: BASIC RULES OF DIFFERENTIATION In Section 3.2, we discussed Rules 1 through 4 below. 0000028357 00000 n Tes Global Ltd is /Filter /FlateDecode � I�C,�A�8��K����4,� �Z6�r� 0000009440 00000 n h��ZYoI�+��U�N߇Yl�8�C��D�x�f�Ⰰh��U=��/�!N"O��U]�UuW�h� %�����%�XxB���A��'#�kxr�(cP�1�N&4V)¤�PЄi��`��,aj�g�C)��p(0�t7�n8�� �j registered in England (Company No 02017289) with its registered office at 26 Red Lion endobj /Length 2596 0000004043 00000 n %���� startxref H�\��j�0��~ 0000025804 00000 n H��W�۸���V$���(�ۤE���4�"(.EAK�Ĭ$:��>�${�u���k[μy3������c(R'B�.�Go���r7z����Hl�����x%I�l�V�q��l�����Z���b�Y_>��X����~�4Y�������E8�N��>}�o��2^�0��9��G����~����w��z��^�9��_賳�c~�h~�u2�?�8�B���7'K\��C/����y���BX5ڏ��G�f��E�Ç��LJ_a6N�Q,�/b��. That is, if c is a real number, then d dx!c"=0. ?���:��0�FB�x$ !���i@ڐ���H���[EE1PL���⢖�V�6��QP��>�U�(j There are certain methods of Educational Technology, 11, p55-56 2 Zakhartchouck, J.M (2004), Au risque de la pédagogie différenciée, INRP. ]�b����]+cF׆��7�tڸ�3���c:�#i>p"�]�:��~p�.�d �"+ 4 . London WC1R 4HQ. 641 0 obj <> endobj 685 0 obj <>/Filter/FlateDecode/ID[]/Index[641 113]/Info 640 0 R/Length 165/Prev 733866/Root 642 0 R/Size 754/Type/XRef/W[1 3 1]>>stream A�ڂ��u��d������;'�ta��ccz~����nߵ���}}��;�]3�k����vٲpM[O�������+K��J��xw��?��,�16ql��{��=��x���n�vM�W������}�����)�����Ct��yIL�7�:Tu���r�^kW���:�]��u3�v��X�����KdeV�g�g�� %PDF-1.4 %���� The “trick” is to differentiate as normal and every time you differentiate a y you tack on a y (from the chain rule). It is convenient to take the logarithm of the function first & then differentiate. endstream endobj 43 0 obj<> endobj 44 0 obj<> endobj 45 0 obj<>stream �'x?��.Pp�j�m��.Q�����3c 33 43 Goal Seek, is easy to use, but it is limited – with it one can solve a single equation, however complicated or however many spreadsheet cells are involved, whether the equation is linear or nonlinear. �ӯ���=�Mθ�;�(ZF�� Implicit Differentiation Find y if e29 32xy xy y xsin 11 . 1 0 obj Lecture by teacher (and what else can you do!) 0000007833 00000 n @~ (* {d+��}�G�͋љ���ς�}W�L��$�cGD2�Q���Z4 E@�@����� �A(�q`1���D ������`'�u�4�6pt�c�48.��`�R0��)� <]>> /N 3 Conditions. 0000045135 00000 n 0000046496 00000 n The underlying function itself (which in this cased is the solution of the equation) is unknown. rA��E�* ��d�KM (x.a 0000008266 00000 n 4. 0000042539 00000 n 0000014427 00000 n 0000046192 00000 n %PDF-1.6 %���� Class discussion conducted by teacher (and what else!) h�bbd```b``e�� �q?���̖`��d����ٹ`v���� Rx;�,�i&g��)$f��H�6�g�g��`��7! Wa�"����Q LOGARITHMIC DIFFERENTIATION : To find the derivative of a function : (a) which is the product or quotient of a number of functions or (b) of the form [f(x)] g (x) where f & g are both derivable. �9�cx��+?L�c�����6M���ٯ�N�p���}0[sm{�/0��{a�1�D|��[��� 0000025218 00000 n ����=�4���@s�9�`4���@g�3�`�x�[)�R�*z���^e��W٫�U�*z���^�V����A��b+�G�Qn��Ji��ƭ[)�Rle�ʰ��o����o����o����o����o��� Mosaic Attenuation: Etiology, Methods of Differentiation, and Pitfalls 1 �"��{V��M��}zCR�J�b��!����m�tr�r�.ф='�6���`��5�+e��[������?��>ì�ᇁ���h&�4_u�� �6����q��g�d��=Uf����I�d 0000010271 00000 n 5. x�b```b``9�������A��X��,3X���*X�K �4����p��}��,�+��є�nq��kXl[T�)g�`��V��2��]�*��,����Z�i�g�Ut)Pp� F~6۹n�Z�r1�hP{��f���U�@�A����@V1))w A�f���Q�ftqK�@H1(�� q�!f���X2�i ��H0�u(�a��P=��(�����8�u�C���y�&NMF���N�;����[�[li�e��x�юM�a��=�b�DGc ��x�)0�4���w Gze� 5 acceptent que les garçons interrompent les filles, et s’adressent à eux avec des phrases courtes et directives. We will investigate f as x → −1 from below (x < −1) and above (x > −1). 0000009900 00000 n 0000002056 00000 n 75 0 obj<>stream 0`�_ck`�)��Ç�=�潇�]��B{�Q� �֣ �GG����[�ت�ci��l����׌zb_ �^ ��\ ��[ �GZ �YJp�PfY�T��F��A��. endstream endobj 34 0 obj<> endobj 35 0 obj<>/MediaBox[0 0 594 774]/TrimBox[0 0 594 774]/Resources<>/ColorSpace<>/Font<>/ProcSet[/PDF/Text/ImageC]/ExtGState<>>>/Type/Page>> endobj 36 0 obj<> endobj 37 0 obj<> endobj 38 0 obj[/ICCBased 55 0 R] endobj 39 0 obj<> endobj 40 0 obj<>stream 0000025638 00000 n 0000002825 00000 n 124 questions for revision practice on methods of differentiation. Later exercises are more advanced and differentiation may require a combination of methods. Learners faced with such challenges would benefit from 0000002655 00000 n �㣄������?����G)���� 1. Consequently, students are failing because they cannot learn well with the methods through which they are being taught. �@���R�t C���X��CP�%CBH@�R����f�[�(t� C��Qh�z#0 ��Z�l�`O8�����28.����p|�O×�X )����f�uu���s�k�`G]��O4�����H肕sI-k�8h��. trailer <> 150 Teaching Methods 1. ���8�H Square 0000025570 00000 n 2 0 obj 0000022814 00000 n h�b```a``�a`c`P+bb@ !�;P�cF1��H�H�D�c�Vi(����x�Ȭ"gw�DAY�yu|W8xj����5�4\�� 0000019224 00000 n endobj 0000044722 00000 n 0 Numerical methods John D. Fenton a pair of modules, Goal Seek and Solver, which obviate the need for much programming and computations. %PDF-1.7 0000040762 00000 n Exercise D involves logarithmic functions and Exercise E is on exponential functions. 0000008647 00000 n 1 Burns, R (1971), Methods for individualizing instruction. %%EOF .��E�#��2�',�$�ň|>>2�&\�p�5�"�B�-5�l���^�5H������$�[���s�� �y�(�a��6�+̬kg��.��-��+�=��利S'a����T.���BSe{j�� �����v���]=���vfpA?��y�e��DS��n��"�T�R����ùiv��Z[���>M�r�r�f�41+�b^���,��8����Tb4�&PE�b���fm��)�:C�eu��LD'1��t�N'�x���4}���B�VM��m���ʠ�;E� Xɑ�߾+0���-I(l!x眗�}�[D�RD@h�k I0�����yR�M�&4�UB͇��� �� |l ye;!�dO��Y$� �1aJ`�WZR)��L��Q,�1X�>��"��_���0L4�B�G�i�^O�ޤ��U��t� �D�S��[��� l�6ٕLI�np�pM�>���������tJ� k.�&$8��OHV%q�/��QU۷�E�N�ܶ�Ed%S�Z}xӲ�M˹��C�,w�I�Ttd�HS��5a�rr�U�!����|u��~]�Rwp��������`xR�R�8D�iz�Ng��ȐӚc���i�L�t��^����d1,T�kB��j H� �6I�>˕T�k���/����>R 0�ʥ�@0�v2}s��uyX�t Z �uM�mLё�%��h`y E,y}PTW��r��q����/dz1���X�h6��mtIb���"r~������ކ2g_��Mh�s�֗��J)a��Yt�/fGXC��b��s�aT( 0000001156 00000 n 33 0 obj <> endobj [/ICCBased 3 0 R] 0000000016 00000 n *1 J�� "6DTpDQ��2(���C��"��Q��D�qp�Id�߼y�͛��~k����g�}ֺ ����LX ��X��ň��g`� l �p��B�F�|،l���� ��*�?�� ����Y"1 P������\�8=W�%�Oɘ�4M�0J�"Y�2V�s�,[|��e9�2��s��e���'�9���`���2�&c�tI�@�o�|N6 (��.�sSdl-c�(2�-�y �H�_��/X������Z.$��&\S�������M���07�#�1ؙY�r f��Yym�";�8980m-m�(�]����v�^��D���W~� ��e����mi ]�P����`/ ���u}q�|^R��,g+���\K�k)/����C_|�R����ax�8�t1C^7nfz�D����p�柇��u�$��/�ED˦L L��[���B�@�������ٹ����ЖX�!

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