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# Note for MATH 263A with Professor Holston at Ohio-section2.3

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Date Created: 02/06/15
Basic Differentiation Formuizs Chris Hoiston Basic Differentiation Formulas Chris Holston Basic Differentiation Formuizs Easy Differentiation Formulas Chris Hoiston Preiiminzries Let c and n be constants Basic Differentiation Formuizs Easy Differentiation Formulas Chris Hoiston Preiiminzries Let c and n be constants d gt 1 ampc0 Basic Differentiation Formuizs Easy Differentiation Formulas Chris Hoiston Preiiminzries Let c and n be constants d gt 1 ampc0 d n n71 gt2 X17HX Basic Differentiation Formuizs Easy Differentiation Formulas Chris Hoiston Preiiminzries Let c and n be constants cl gt1c0 d n n71 gt2 X17HX cl gt 3 amp5Inx cosx Basic Differentiation Formuizs Easy Differentiation Formulas Chris Hoiston Preiiminzries Let c and n be constants cl gt1c0 d n n71 gt2 X17HX cl gt 3 amp5Inx cosx cl gt 4 cosx 75InX Basic Differentiation Formuizs Recursive Formulas Chris Hoiston Preiiminzries Let c be a constant and g be differentiable functions d gt 1 cfx cf X Basic Differentiation Formuizs Recursive Formulas Chris Hoiston Preiiminzries Let c be a constant and g be differentiable functions d gt 1 cfx cf X gt 2 lm igun f x igx Basic Differentiation Formuizs Applications Chris Hoiston Preiiminzries If 5t represents a position function then Basic Differentiation Formuizs Applications Chris Hoiston Preiiminzries If 5t represents a position function then s t vt is the velocity function and Basic Differentiation Formulas Applications cm Holston Preliminaries f 5t represents a position function then s t vt is the velocity function and s t v t at is the acceleration function Basic Differentiation Formulas Applications cm Holston Preliminaries f 5t represents a position function then s t vt is the velocity function and s t v t at is the acceleration function The tangent line to a function f at a is given by y 7 fa f axi 3 provided f a exists Basic Differentiation Formulas Applications cm Holston Preliminaries f 5t represents a position function then s t vt is the velocity function and s t v t at is the acceleration function The tangent line to a function f at a is given by y 7 fa f axi 3 provided f a exists The normal line to a function f at a is given by 71 y 7 fa fake 3 provided f a exists and is nonzero Basic Differentiation Formulas Applications cm Hoiston Preliminaries f 5t represents a position function then s t vt is the velocity function and s t v t at is the acceleration function The tangent line to a function f at a is given by y 7 fa f axi 3 provided f a exists The normal line to a function f at a is given by 71 y 7 fa 7 wki a prOVIded f a eXIsts and IS nonzero In other words it is the line crossing the function at a and perpendicular to the tangent line Basic Differentiation Formuizs Chris Hoiston 8 Exam ses Differentiate the function y sint 7r cost Basic Differentiation Formuizs Chris Hoiston 8 Exam ses Differentiate the function y sint 7r cost dy a cost 7 7r sint Basic Differentiation Formuizs Chris Hoiston Exerci ses Differentiate the function hx X 7 22X 3 Basic Differentiation Formuizs Chris Hoiston Exerci ses Differentiate the function hx X 7 22X 3 h x 4x71 Basic Differentiation Formuizs Chris Hoiston Exerci ses Differentiate the function V10 R 7 Basic Differentiation Formuizs Chris Hoiston Exerci ses Differentiate the function V10 R 7 Basic Differentiation Formuizs Chris Hoiston Exerci ses Differentiate the function gu xiuPE Basic Differentiation Formuizs Chris Hoiston Exerci ses Differentiate the function gu xiu xPE 00 Z Basic Differentiation Formuizs Chris Hoiston Exerci ses Differentiate the function 7 x2 7 2V X Basic Differentiation Formuizs Chris Hoiston Exerci ses Differentiate the function 7 x2 7 2V 7 x dy 1 71 7 dx x Basic Differentiation Formuizs Chris Hoiston Exerci ses Differentiate the function sin9 c 2 6 Basic Differentiation Formuizs Chris Hoiston Exerci ses Differentiate the function sin9 c 2 6 7 cos6 7 c d 97 2 62 Basic Differentiation Formuias Chris Hoiston Exerci 595 Find equations of the tangent line and normal line to the curve at the given point y 1 2X27179 Basic Differentiation Formuias Chris Hoiston Exerci 595 Find equations of the tangent line and normal line to the curve at the given point y 1 2X27179 tangent line y 12x 7 3 Basic Differentiation Formuias Chris Hoiston Exerci 595 Find equations of the tangent line and normal line to the curve at the given point y 1 2X27179 tangent line y 12x 7 3 1 109 normal line y i x f Basic Differentiation Formulas Chris Holston Exerci 595 If a ball is given a push so that it has an initial velocity of 5 ms down a certain inclined plane then the distance it has rolled after 1 seconds is s 5139 31392 a Find the velocity after 2 s b How long does it take for the velocity to reach 35 ms Basic Differentiation Formulas Chris Holston Exerci 595 If a ball is given a push so that it has an initial velocity of 5 ms down a certain inclined plane then the distance it has rolled after 1 seconds is s 5139 31392 a Find the velocity after 2 s b How long does it take for the velocity to reach 35 ms a v2 17 ms Basic Differentiation Formulas Chris Holston Exerci 595 If a ball is given a push so that it has an initial velocity of 5 ms down a certain inclined plane then the distance it has rolled after 1 seconds is s 5139 31392 a Find the velocity after 2 s b How long does it take for the velocity to reach 35 ms a v2 17 ms b t 5 s

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