Explanation Given: The provide function is f ( x , y ) = ( x + y 2 ) 2 x + y . Approach: The partial derivative of f ( x , y ) with respect to x is, f x ( x , y ) = ∂ ∂ x f ( x , y ) = lim h → 0 f ( x + h , y ) − f ( x , y ) h Calculation: Consider the given function, f ( x , y ) = ( x + y 2 ) 2 x + y The value of function f ( x , y ) and ( 2 , 1 ) . f ( 2 , 1 ) = ( 2 + 1 2 ) 2 ( 2 ) + 1 = ( 3 ) 5 = 243 The value of function f ( x , y ) and ( 2 + h , 1 ) . To determine (b) To find: The approximation the derivate f y ( 2 , 1 ) for function f ( x , y ) = ( x + y 2 ) 2 x + y by using the definition of the derivative with small values of h .

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 9.2, Problem 48E

To determine

(a)

To find:

The approximation the derivate fx(2,1) for function f(x,y)=(x+y2)2x+y by using the definition of the derivative with small values of h.

To determine

(b)

To find:

The approximation the derivate fy(2,1) for function f(x,y)=(x+y2)2x+y by using the definition of the derivative with small values of h.

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Chapter 9.2, Problem 47E

Chapter 9.2, Problem 49E

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Chapter 9 Solutions

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

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(a) To find: The approximation the derivate f x ( 2 , 1 ) for function f ( x , y ) = ( x + y 2 ) 2 x + y by using the definition of the derivative with small values of h .

Solution Summary: The author explains how to find the approximation of the derivate f_x(2,1) by using the definition of a derivative with small values.

Videos

(a)

To find:

The approximation the derivate fx(2,1) for function f(x,y)=(x+y2)2x+y by using the definition of the derivative with small values of h.

(b)

To find:

The approximation the derivate fy(2,1) for function f(x,y)=(x+y2)2x+y by using the definition of the derivative with small values of h.

Want to see the full answer?

Chapter 9 Solutions

(a) To find: The approximation the derivate f x ( 2 , 1 ) for function f ( x , y ) = ( x + y 2 ) 2 x + y by using the definition of the derivative with small values of h .

Solution Summary: The author explains how to find the approximation of the derivate f_x(2,1) by using the definition of a derivative with small values.

Videos

(a) To find: The approximation the derivate fx(2,1) for function f(x,y)=(x+y2)2x+y by using the definition of the derivative with small values of h.

(b) To find: The approximation the derivate fy(2,1) for function f(x,y)=(x+y2)2x+y by using the definition of the derivative with small values of h.

Want to see the full answer?

Chapter 9 Solutions

(a)

To find:

The approximation the derivate fx(2,1) for function f(x,y)=(x+y2)2x+y by using the definition of the derivative with small values of h.

(b)

To find:

The approximation the derivate fy(2,1) for function f(x,y)=(x+y2)2x+y by using the definition of the derivative with small values of h.