please Show work.

Sol: (1) (a)   23y x x x  
On taking a differentiation of y with respect to ,x
   
     
2
3 2 2
3 2
3 2
2

3
3 3
4 3
4 3
3 8 3
dy d
x x x
dx dx
d
x x x x
dx
d
x x x
dx
d d d
x x x
dx dx dx
dy
x x
dx
   
 
     
    
  
  
Sol: (1) (b)
 
 
3
2
1
4
x
y
x




On taking a differentiation of y with respect to ,x
 
 
       
 
       
 
   
 
 
3
2
2 3 3 2
2
2
2 2 3
2
2
4 2 4
2
2
4 2
2
2
1
4
4 1 1 4
4
4 3 1 2
4
3 12 2 2
4
12 2
4
xdy d
dx dx x
d d
x x x x
dx dx
x
x x x x
x
x x x x
x
dy x x x
dx x
 
 
  
    


  


  


 


Sol: (2) (a)  2y x x 
On taking a differentiation of y with respect to ,x
 
 
   
 
 
 
 
2
1 2
2
1 2
2
1 2
2
2
1
2 1
2
1 1
2 1
2
2 11
2
dy d
x x
dx dx
d
x x
dx
x x x
x
x x
xdy
dx x x

 
 
  
 




Sol: (2) (b)  
5
4 2y x x 
On taking a differentiation of y with respect to ,x
 
   
   
   
5
4 2
5 1
4 2 4 2
4
4 2 4 2
4
4 2 3
5
5
5 4 2
dy d
x x
dx dx
d
x x x x
dx
d
x x x x
dx
dy
x x x x
dx

 
  
  
  
Sol: (3)
 
 
   
   
   
   
   
   
2
3 2
2 33
2 6 4 2
2 3 2 33
2 3 4 2
2 3 2 3
2 3 2 32 3 4 2
2 3 2...