Solution - Simplification or other simple results

Step  1  :

             d
 Simplify   ——
            dx

Canceling Out :

 1.1    Canceling out d as it appears on both sides of the fraction line

Equation at the end of step  1  :

   1
  (— • (x + 1)) • (x + 1)
   x

Step  2  :

Equation at the end of step  2  :

  (x + 1)
  ——————— • (x + 1)
     x   

Step  3  :

Multiplying Exponential Expressions :

 3.1    Multiply  (x+1)  by  (x+1) 

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (x+1)  and the exponents are :
          1 , as  (x+1)  is the same number as  (x+1)¹ 
 and   1 , as  (x+1)  is the same number as  (x+1)¹ 
The product is therefore,  (x+1)⁽¹⁺¹⁾ = (x+1)² 

Final result :

  (x + 1)2
  ————————
     x