Chap14_Sec3

Chap14_Sec3 - PARTIAL DERIVATIVES 14.3 Partial Derivatives...

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14.3 Partial Derivatives PARTIAL DERIVATIVES In this section, we will learn about: Various aspects of partial derivatives.
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If f is a function of two variables, its partial derivatives are the functions f x and f y defined by: There are many alternative notations for partial derivatives. or instance, instead of we can write r o indicate 0 0 ( , ) ( , ) ( , ) lim ( , ) ( , ) ( , ) lim x h y h f x h y f x y f x y h f x y h f x y f x y h + - = + - = PARTIAL DERIVATIVES s For instance, instead of f x , we can write f 1 or D 1 f (to indicate differentiation with respect to the first variable) or f / x . s However, here, f / x can’t be interpreted as a ratio of differentials. If z = f ( x , y ), we write: 1 1 2 2 ( , ) ( , ) ( , ) ( , ) x x x y y y f z f x y f f x y x x x f D f D f f z f x y f f x y y y y f D f D f = = = = = = = = = = = = = =
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RULE TO FIND PARTIAL DERIVATIVES OF z = f ( x , y ) 1. To find f x , regard y as a constant and differentiate f ( x , y ) with respect to x . 2.
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Chap14_Sec3 - PARTIAL DERIVATIVES 14.3 Partial Derivatives...

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