The derivative rules that have been presented in the last several sections are collected together in the following tables. DERIVATIVE RULES d ()xnnxn1 dx = − ()sin cos d x x dx = ()cos sin d x x dx =− d ()aax ln x dx =⋅a ()tan sec2 d x x dx = ()cot csc2 d x x dx =− ()() () () d f xgx fxgx gx fx dx ⋅=⋅ +⋅′′ ()sec sec tan d x x dx = x ()csc csc cot d x xx dx =− ()2 dfx gxfx fxgx << /S /GoTo /D [2 0 R /Fit ] >> Find an equation for the tangent line to f(x) = 3x2 −π3 at x = 4. Power Rule: d dx (xn) = nxn 1 3. ��P&3-�e�������l�M������7�W��M�b�_4��墺�݋�~��24^�7MU�g� =?��r7���Uƨ"��l�R�E��hn!�4L�^����q]��� #N� �"��!�o�W��â���vfY^�ux� ��9��(�g�7���F��f���wȴ]��gP',q].S϶z7S*/�*P��j�r��]I�u���]� �ӂ��@E�� /Length 2424 Chain Rule: : ; . %PDF-1.4 Product Rule: (fg)0 = f0g +fg0 4. Product rule: (fg)0= f 0g + fg Reciprocal rule: 1 g 0 = g0 g2 Quotient rule: f g 0 = f0g 0fg g2 A more complete statement of the product rule would assume that f and g are di er-entiable at x and conlcude that fg is di erentiable at x with the derivative (fg)0(x) equal to f0(x)g(x) + f(x)g0(x). Derivative Rules: :Power Rule: . t\d�8C�B��$q"*��i���JG�3UtlZI�A��1^���04�� ��@��*io���\67D����7#�Hbm���8�齷D�`t���8oL �6"��>�.�>����Dq3��;�gP��S��q�}3Q=��i����0Aa+�̔R^@�J?�B�%�|�O��y�Uf4���ُ����HI�֙��6�&�)9Q`��@�U8��Z8��)�����;-Ï�]x�*���н-��q�_/��7�f�� Derivatives Cheat Sheet Derivative Rules 1. stream 5 0 obj << Suppose the position of an object at time t is given by f(t) = −49t2/10 + 5t + 10.Find a function giving the speed of the object at time t. Quotient Rule: f g 0 = f0g 0fg g2 5. :=0 2Sum/Difference Rule: : ± ;′= ′± ;Constant Out: ′ :⋅ ′=⋅ Product Rule: : ⋅ ;′= ′⋅ + ′ Quotient Rule: @ . x��ZKs�F��W`Ok�ɼI�o6[q��։nI0 IȂ�L����{xP H;��R����鞞�{@��f�������LrM�6�p%�����%�:�=I��_�����V,�fs���I�i�yo���_|�t�$R��� ;=⋅−1. /Filter /FlateDecode �7�2�AN+���B�u�����@qSf�1���f�6�xv���W����pe����.�h. ;Derivative of a Constant: . ��gUFvE�~����cy����G߬֋z�����1�a����ѩ�Dt����* ��+彗a��7������1릺�{CQb���Qth�%C�v�0J�6x�d���1"LJ��%^Ud6�B�ߗ��?�B�%�>�z��7�]iu�kR�ۖ�}d�x)�⒢�� 1 0 obj = . endobj Constant Rule: d dx (c) = 0; where c is a constant 2. >> 3. fg f g fg – Product Rule 4. ⇒ 9. A. 60 Chapter 3 Rules for Finding Derivatives 8. ⋅ . 2 ffgfg gg – Quotient Rule 5. 0 d c dx 6. nn1 d xnx dx – Power Rule 7. d fgx f gx g x dx This is the Chain Rule Common Derivatives 1 d x dx sin cos d xx dx cos sin d xx dx tan sec2 d xx dx sec sec tan d xxx dx csc csc cot d xxx dx %����

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