differentiating using quotient rule

Question

1.   y=(x-3)²/(x+2)²      2.     x/√(1-x²)

Answer 1

The quotient rule:

 

Bottom*d(Top) - Top*d(Bottom)

               (Bottom)²

 

1.  y =        (x - 3)²           

                  (x + 2)²

 

(x+2)²*d[(x-3)²] - (x-3)²*d[(x+2)²]

                    (x+2)⁴

 

(x+2)² * 2(x-3) - (x-3)² *2(x+2)

                   (x+2)⁴

 

 

 

2.           x       

          (1-x²)^1/2

 

(1-x²)^1/2 * d/dx (x) - x * d/dx [(1-x²)^1/2]

                 [(1-x²)^1/2]²

 

(1-x²)^1/2 - x*(1/2)(1-x²)^-1/2

              (1-x²)