differentiation1a_adj - ECON1003 Mathematics for the Social...

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1 ECON1003 Mathematics for the Social Sciences Topic 8: Differentiation Lecturer: Marlon Tracey
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2 Objective o At the end of this topic, students should be able to: o Define the concept of differentiation. o Evaluate the differential of a function from first principles. o Identify and apply the rules of differentiation to various functions. o Determine the gradient of a function through differentiation.
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3 Outline o The concept of differentiation o Differentiation from first principles o Rules of differentiation o Differential of exponential and logarithmic functions o Computing the gradient of a function
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4 Concept of differentiation I o Differentiation is a technique in calculus used to find “ rates of change ” or “ the slope of a function ” or the rate at which y changes as x changes ” or “ how steeply a curve rises at a point x ”. source: math tutor Graph of the slope of a function at a point x y
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5 Concept of differentiation II o The value or expression that results after differentiation has been applied to a function is referred to as the derivative or the differential. o We use the symbol or to mean “the derivative of y with respect to x”. We also use to mean the derivative of f with respect to x”. o From analyzing the graph on the previous slide, it was realized that the slope or derivative of the function y = 3x + 2 is 3. In calculus, we simply write this as: dx dy 3 = dx dy y ) ( ' x f
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This note was uploaded on 03/16/2011 for the course ECON 1003 taught by Professor Dr.mcdonald during the Spring '11 term at University of the West Indies at Mona.

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differentiation1a_adj - ECON1003 Mathematics for the Social...

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