x ----------- ________ / 2 \/ x - 1
d / x \ --|-----------| dx| ________| | / 2 | \\/ x - 1 /
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 1 x ----------- - ----------- ________ 3/2 / 2 / 2 \ \/ x - 1 \x - 1/
/ 2 \ | 3*x | x*|-3 + -------| | 2| \ -1 + x / ---------------- 3/2 / 2\ \-1 + x /
/ / 2 \\ | 2 | 5*x || | x *|-3 + -------|| | 2 | 2|| | 3*x \ -1 + x /| 3*|-1 + ------- - -----------------| | 2 2 | \ -1 + x -1 + x / ------------------------------------ 3/2 / 2\ \-1 + x /