Given: 1 p p * i rG z (z) 1 (c w )z p (z w ) + -? a + + ß = and 1 F(z) 1 (c w ) 1 z (z) z p - = ß a...

Question

Given: 1 p p * i rG z (z) 1 (c w )z p (z w ) + -? a + + ß = and 1 F(z) 1 (c w ) 1 z (z) z p - = ß a + + -? Find the derivative of ps with respect to wp. Note that z is a function of wp and ps is a function of both wp and z. p s(wp ) =[wp - c(1-a1 -a2 )][ae(-ß+? ) p (2z)] 2. Plot wp vs. ?
	
Document Preview: 1.	  Given:	  
	  
(ca +w )z
1
p
*
p (z w )= + +rG
i p 1
ß z -?(z)
 	  
and
 
z 1 1
+ =
z-?(z) ß(ca +w ) 1-F(z)
p
	  
	  
Find	  the	  derivative	  of	  ps	  with	  respect	  to	  wp.	  Note	  that	  z	  is	  a	  function	  of	  wp	  and	  ps	  is	  
a	  function	  of	  both	  wp	  and	  z. 
 
(-ß+?)p
p (w )=[w -c(1-a -a )][ae (2z)]
s p p 1 2
	  
	  
2.	  Plot	  wp	  vs.	  ?

Robert · Accepted Answer

Solution 1: 
Here are given equations 
   (
 
  
)
 
 
(     ) 
   ( )
    ---------------------------------- say equ. (1)
   ( )

 (     )

   ( )
  --------------------------------------say equ. (2) 
Also given that 
 ( )         and  ( )      
By substituting above in equ. (2), we can find the variable z with respect to    
z =  √
   (     )
    (     )
  ---------------------------------------------say equ. (3) 
By substituting  ( ) in equ. (1) 
   (
 
  
)
 
  (     )      ----------------------------say equ. (4) 
Now we need to find the derivative of  
  (  )  [    (       )]   
 (   )  (  )   
By substituting equ. (3) and (4) in the above equation we get 
  (  )  [    (       )]   
 (   )(
 
 
  (     )    )  ( √
   (     )
    (     )
  )   
This implies 
  (  )  
*  √
   (     )
    (     )
  
(   )( (  ))  
 (       )√
   (     )
    (     )
  
(   )( (  ))+     
 (   )(
 
 
  (  )    )
   – say        equ 
(5) 
Here given that c, beta, alpha, r,

Given: 1 p p * i rG z (z) 1 (c w )z p (z w ) + -? a + + ß = and 1 F(z) 1 (c w ) 1 z (z) z p - = ß a + + -? Find the derivative of ps with respect to wp. Note that z is a function of wp and ps is a...

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