1 1*----------- ________ / 2 \/ 1 - x
d / 1 \ --|1*-----------| dx| ________| | / 2 | \ \/ 1 - x /
Apply the quotient rule, which is:
and .
To find :
The derivative of the constant is zero.
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.
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
The result is:
The result of the chain rule is:
Now plug in to the quotient rule:
The answer is:
x -------------------- ________ / 2\ / 2 \1 - x /*\/ 1 - x
/ 2 \ | 3*x | -|-1 + -------| | 2| \ -1 + x / ---------------- 3/2 / 2\ \1 - x /
/ 2 \ | 5*x | -3*x*|-3 + -------| | 2| \ -1 + x / ------------------- 5/2 / 2\ \1 - x /