2 x -------- 2 (x + 2)
x^2/(x + 2)^2
Apply the quotient rule, which is:
and .
To find :
Apply the power rule: goes to
To find :
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
The derivative of the constant is zero.
Apply the power rule: goes to
The result is:
The result of the chain rule is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
2 2*x x *(-4 - 2*x) -------- + ------------- 2 4 (x + 2) (x + 2)
/ 2 \ | 4*x 3*x | 2*|1 - ----- + --------| | 2 + x 2| \ (2 + x) / ------------------------ 2 (2 + x)
/ 2 \ | 2*x 3*x | 12*|-1 - -------- + -----| | 2 2 + x| \ (2 + x) / -------------------------- 3 (2 + x)