___ /x\ \/ 3 *x*cos|-| \3/
d / ___ /x\\ --|\/ 3 *x*cos|-|| dx\ \3//
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the product rule:
; to find :
Apply the power rule: goes to
; to find :
Let .
The derivative of cosine is negative sine:
Then, apply the chain rule. Multiply by :
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 of the chain rule is:
The result is:
So, the result is:
Now simplify:
The answer is:
___ /x\ x*\/ 3 *sin|-| ___ /x\ \3/ \/ 3 *cos|-| - -------------- \3/ 3
___ / /x\ /x\\ -\/ 3 *|6*sin|-| + x*cos|-|| \ \3/ \3// ----------------------------- 9
___ / /x\ /x\\ \/ 3 *|- 9*cos|-| + x*sin|-|| \ \3/ \3// ----------------------------- 27