The Quotient Rule: Solutions

1. 
   
   
   In this case, it's quite convenient to note that the derivative of the numerator and denominator are the same, so that the quotient rule reduces to
   

2. 
   
   
   This is a sum of terms of the form x^-n, where n = 0, 1, 2, 3. The derivative is then
   

3. 
   
   
   The derivative of the numerator is zero, so the chain rule reduces to