x ----------- ________ / 2 \/ x + 1
x/sqrt(x^2 + 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 /