Lesson 8 Higher Order and Implicit Differentiation

Lesson 8 Higher Order and Implicit Differentiation - HIGHER...

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HIGHER DERIVATIVES AND IMPLICIT DIFFERENTIATION
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OBJECTIV ES : to define higher derivatives; to apply the knowledge of higher derivatives and implicit differentiation in proving relations; to find the higher derivative of algebraic functions; and to determine the derivative of algebraic functions implicitly under the specified conditions.
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The derivative of a function f is itself a function and hence may have a derivative of its own. If is differentiable, then its derivative is denoted by and is called the second derivative of f. As long as we have differentiability, we can continue the process of differentiating to HIGHER DERIVATIVES ,...... )' ( , )' ' ' ' ( , )' ' ' ( ' ' ' , )' ' ( ' ' , ' 4 5 4 f f f f f f f f f = = = = These successive derivatives are denoted by ' f ' f " f
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Other common notations for higher derivatives are the following: first derivative: ) ( ), ( ), ( ' , ' , x f D x f dx d x f y dx dy x second derivative: ) ( ), ( ), ( ' ' , ' ' , 2 2 2 2 2 x f
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Lesson 8 Higher Order and Implicit Differentiation - HIGHER...

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