Quiz 2 Quiz 2                              Friday, March 16, 2001



NAME:

Student Number:------            No.----           Marks ----






(25 Marks) Find the derivative of f(x) = {[(x2+1)/(x4+1)]}.

Solution. 1. Applying ln to the equation f(x) = {[(x2+1)/(x4+1)]}, we obtain


lnf(x)
=
ln   
 


x2+1
x4+1
 
= ln
x2+1
x4+1

1/2
 
=
1
2
ln x2+1
x4+1
= 1
2

ln(x2+1)-ln(x4+1)
.

Taking the derivative of this equation, we have


1
f(x)
f(x) = 1
2

2x
x2+1
- 4x3
x4+1

.

This implies


f(x)
=
f(x) 1
2

2x
x2+1
- 4x3
x4+1

= 1
2
  
 


x2+1
x4+1
 

2x
x2+1
- 4x3
x4+1

=
  
 


x2+1
x4+1
 

x
x2+1
- 2x3
x4+1




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On 3 Apr 2001, 10:30.