3 / 1\ x *sin|1*-| \ x/
d / 3 / 1\\ --|x *sin|1*-|| dx\ \ x//
Apply the product rule:
; to find :
Apply the power rule: goes to
; to find :
Let .
The derivative of sine is cosine:
Then, apply the chain rule. Multiply by :
Apply the quotient rule, which is:
and .
To find :
The derivative of the constant is zero.
To find :
Apply the power rule: goes to
Now plug in to the quotient rule:
The result of the chain rule is:
The result is:
Now simplify:
The answer is:
/ 1\ 2 / 1\ - x*cos|1*-| + 3*x *sin|1*-| \ x/ \ x/
/1\ sin|-| /1\ \x/ /1\ - 4*cos|-| - ------ + 6*x*sin|-| \x/ x \x/
/1\ /1\ cos|-| 6*sin|-| / /1\\ /1\ \x/ \x/ | sin|-|| - 6*cos|-| + ------ + -------- /1\ | /1\ \x/| \x/ 2 x 18*cos|-| 9*|2*cos|-| - ------| /1\ x \x/ \ \x/ x / 6*sin|-| + ------------------------------ - --------- + --------------------- \x/ x x x