Apply the product rule:
; 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.
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:
The result is:
Now simplify:
The answer is:
__________ 2 / 2 2*x \/ 3 - 2*x - ------------- __________ / 2 \/ 3 - 2*x
/ 2 \ | 2*x | 2*x*|-3 + ---------| | 2| \ -3 + 2*x / -------------------- __________ / 2 \/ 3 - 2*x
/ 2 \ / 2 \ | 2*x | | 2*x | 6*|1 + --------|*|-1 + ---------| | 2| | 2| \ 3 - 2*x / \ -3 + 2*x / --------------------------------- __________ / 2 \/ 3 - 2*x