Suppose f is a differentiable function of x and y, and g(r, s) = f(2r − s, s2 − 7r). Use the table of values below to calculate gr(4, 3) and gs(4, 3). f g fx fy (5, −19) 4 9 7 1 (4, 3) 9 4 5 2 gr(4, 3) = gs(4, 3) =

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2021-11-03

Suppose f is a differentiable function of x and y, and 

g(rs) = f(2r − ss2 − 7r).

 Use the table of values below to calculate 

gr(4, 3)

 and 

gs(4, 3).

    f     g     fx     fy  

  (5, −19)  

4

9

7

1

  (4, 3)  

9

4

5

2

 

gr(4, 3)  =   
gs(4, 3)  = 
Suppose f is a differentiable function of x and y, and 

g(rs) = f(2r − ss2 − 7r).

 Use the table of values below to calculate 

gr(4, 3)

 and 

gs(4, 3).

    f     g     fx     fy  

  (5, −19)  

4

9

7

1

  (4, 3)  

9

4

5

2

 
gr(4, 3)  =   
gs(4, 3)  = 
Suppose f is a differentiable function of x and y, and 

g(rs) = f(2r − ss2 − 7r).

 Use the table of values below to calculate 

gr(4, 3)

 and 

gs(4, 3).

    f     g     fx     fy  

  (5, −19)  

4

9

7

1

  (4, 3)  

9

4

5

2

 
gr(4, 3)  =   
gs(4, 3)  = 

 

 

 

Answer & Explanation

RizerMix

RizerMix

Expert2023-04-20Added 656 answers

To find gr(4,3), we need to differentiate g with respect to r while holding s constant. Using the chain rule, we have:

gr=gr=fx(2r-s)r+fy(s2-7r)r

=fx(2)-fy(7)

Substituting the values from the table, we have:

gr(4,3)=fx(2)-fy(7)=5(2)-2(7)=-4

To find gs(4,3), we need to differentiate g with respect to s while holding r constant. Using the chain rule, we have:

gs=gs=fx(2r-s)s+fy(s2-7r)s

=-fx(1)+fy(6)

Substituting the values from the table, we have:

gs(4,3)=-fx(1)+fy(6)=-7(1)+2(6)=5

Therefore, gr(4,3)=-4 and gs(4,3)=5.

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