Differentiation Formulas – Here we will start introducing some of the differentiation formulas used in a calculus … • (c)’=0 • The derivative of a constant is zero. • ′ =× ′( ) • The derivative of a function multiplied by a constant is the constant multiplied by the derivative. stream ?v�"U���X�[;���(. What are Derivatives? 20 0 obj Quality links from around the web. But in practice the usual way to find derivatives is to use: Derivative Rules . Differentiation Formulas – In this section we give most of the general derivative formulas and properties used when taking the derivative of a function. Suppose the position of an object at time t is given by f(t) = −49t2/10 + 5t + 10.Find a function giving the speed of the object at time t. Knowing implicit differentiation will allow us to do one of the more important applications of derivatives, Related Rates (the next section)./p>. The Chain Rule52 14. 4. Derivatives of Exponential and Logarithm Functions – In this section we derive the formulas for the derivatives of the exponential and logarithm functions. � T���f�``��``�b����``@PL&kst40Y@��q0�gFL��@�
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We show the derivation of the formulas for inverse sine, inverse cosine and inverse tangent. When taking the derivative of any term that has a “y” in it multiply the term by y0 (or dy=dx) 3. %PDF-1.5 Solve for y0 When ﬁnding the second derivative y00, remember to replace any y0 terms in your ﬁnal answer with the equation for y 0you already found. Related Rates – In this section we will discuss the only application of derivatives in this section, Related Rates. Rate of Change. x��ZK��v�����&�nDC�,>��؆���,�C��,�$�Ү�l��T��,v�gW��0���QU���"_�PGI����^��O������A���ϣ��.p@8#�s�xr��QG:��"��ŋÿ&�ORX�@�_�#M�F��M����Rh��������4���yZD+ q���.B�az3� a��d>iG�0]� You appear to be on a device with a "narrow" screen width (, Derivatives of Exponential and Logarithm Functions, L'Hospital's Rule and Indeterminate Forms, Substitution Rule for Indefinite Integrals, Volumes of Solids of Revolution / Method of Rings, Volumes of Solids of Revolution/Method of Cylinders, Parametric Equations and Polar Coordinates, Gradient Vector, Tangent Planes and Normal Lines, Triple Integrals in Cylindrical Coordinates, Triple Integrals in Spherical Coordinates, Linear Homogeneous Differential Equations, Periodic Functions & Orthogonal Functions, Heat Equation with Non-Zero Temperature Boundaries, Absolute Value Equations and Inequalities. y = f(x) and yet we will still need to know what f'(x) is. The Di erentiation Rules45 7. Example: what is the derivative of sin(x) ? This chapter is devoted almost exclusively to finding derivatives. Exercises44 6. Derivatives (2)41 1. %�쏢 calculus_midyear_exam_review_part_iv_solutions.pdf: File Size: 268 kb: File Type: pdf: Download File. Some non-di erentiable functions43 5. Wednesday 1/22-1/23: Review Tuesday 1/21: 1st Derivative Test Practice Thursday 1/16: 1st Derivative Test Wednesday 1/15: NO HW. Exercises49 9. Exercises51 11. This is often one of the more difficult sections for students. We will be looking at one application of them in this chapter. x��Zے�}�W�O��,wv*���q9q*�wǕ̓F��,QZR���}N Ej���]�R{�E@��}�J���Č㏘��l����1笚=��Br&��v�m�?mf�f��>����/b&r&�ѳ���ВY!ge���f������l��P-7��. Derivatives De ned41 2. =�ꆀ��N�Ay�\�}BE�*(����Ӯm�"Ӈ��`�A��xOʷ5˘p!r�_.>Ą[��!��c�=$@R�*�h���λ� there are variables in both the base and exponent of the function. <> ifferential Calculus Paul chrimpf ctober 31, 2018 niversity of ritish Columbia conomics 526 1 In this lecture, we will deﬁne derivatives for functions on vector spaces. 133 0 obj
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The files are available in portable document format (pdf) or in postscript (ps). Fractional calculus is when you extend the definition of an nth order derivative (e.g. 5 0 obj ����͇Ǡ����d?�r8�T� g��|�Rk�{�����fu���p6�P�4Js��4����&ds�]Q�h��u!�-tM߂P�G���&�����"�O@�^.k�U�V'� ���h��jH�bY帀eUݷ��!�ƦY[�}��&���=���I���D���_g�=�O_ZrR�Y�331��d��n?�n1�ؖ��uM�{�tt���glC�@H�q'����A�qSԶ�EA2��Z��O6�����xB�H�$�
�Ϗ����������h�nc}ڒ���$���3�z�ʞB�G�u�r�P��.�lU���^��5��Z>m,�T�u���=��� Here is a listing of the topics covered in this chapter. �`�rV�Y���[�l!��8��F��i�nt�@L�)aL]@Km�w�R�Lg-P��_H�7#
Derivatives of Hyperbolic Functions – In this section we define the hyperbolic functions, give the relationships between them and some of the basic facts involving hyperbolic functions.

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