Lesson 10 Differentials - THE DIFFERENTIALS Objectives At...

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THE DIFFERENTIALS
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Objectives At the end of the discussion, the students , at the minimum, should be able to : - Differentiate derivatives and differentials - Determine the differentials of functions - Find the derivative of parametric equations
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The derivative of a function can often be used to approximate certain function values with a surprising degree of accuracy. To do this, the concept of the differential of the independent variable and the dependent variable must be introduced. ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 x f x x f x x ' f ly equivalent or x x f x x f x f' is That . x f x, through line secant the of slope the as same the ely approximat is tangent the of slope the then , 0 x very small is x If . x f x, point some at curve the to line tangent the of slope the represents ich wh x x f x x f lim x f' is recall you as x f y function a of derivative the of definition The 0 x - + - + - + = =
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( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 y dx x f' dy therefore x f - x x f y Because x
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