Explanation Approach: Let z = f ( x , y ) be a function of two independent variables. Let all indicated limits exist. Then the partial derivative of f with respect to x is, f x ( x , y ) = ∂ f ∂ x And the partial derivative with respect to y is, f y ( x , y ) = ∂ f ∂ y Also, ∂ ∂ x [ f ( x ) g ( x ) ] = g ( x ) ∂ f ( x ) ∂ x − f ( x ) ∂ g ( x ) ∂ x g ( x ) 2 Calculation: Consider the function, f ( x , y ) = 3 x 2 x − y ... ( 1 ) Differentiate equation ( 1 ) with respect to x and keep y constant. f x ( x , y ) = ∂ ∂ x [ 3 x 2 x − y ] = ( 2 x − y ) ⋅ 3 − 3 x ⋅ 2 ( 2 x − y ) 2 = − 3 y ( 2 x − y ) 2 ... ( 2 ) Differentiate equation ( 2 ) with respect to x and keep y constant.

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

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Chapter 9.CR, Problem 39CR

To determine

To find:

The value of fxx(x,y) and fxy(x,y) if f(x,y)=3x2x−y.

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Chapter 9.CR, Problem 38CR

Chapter 9.CR, Problem 40CR

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Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

Ch. 9.1 - YOUR TURN For the function in Example 1, find...Ch. 9.1 - Prob. 2YT Ch. 9.1 - Prob. 3YT Ch. 9.1 - EXERCISES Let f(x,y)=2x3y+5.Find the following. a....Ch. 9.1 - Prob. 2E Ch. 9.1 - EXERCISES Let h(x,y)=x2+2y2. Find the following....Ch. 9.1 - EXERCISES Let f(x,y)=9x+5ylogx. Find the...Ch. 9.1 - EXERCISES Let f(x,y)=ex+ln(x+y). Find the...Ch. 9.1 - EXERCISES Let f(x,y)=xex+y. Find the following. a....Ch. 9.1 - EXERCISES Let f(x,y)=xsin(x2y). Find the...

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