2 (x - 2) -------- x + 1
(x - 2)^2/(x + 1)
Apply the quotient rule, which is:
and .
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:
To find :
Differentiate term by term:
The derivative of the constant is zero.
Apply the power rule: goes to
The result is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
2 -4 + 2*x (x - 2) -------- - -------- x + 1 2 (x + 1)
/ 2 \ | (-2 + x) 2*(-2 + x)| 2*|1 + --------- - ----------| | 2 1 + x | \ (1 + x) / ------------------------------ 1 + x
/ 2 \ | (-2 + x) 2*(-2 + x)| 6*|-1 - --------- + ----------| | 2 1 + x | \ (1 + x) / ------------------------------- 2 (1 + x)