2 2 x *sin (x)
d / 2 2 \ --\x *sin (x)/ dx
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 :
The derivative of sine is cosine:
The result of the chain rule is:
The result is:
Now simplify:
The answer is:
2 2 2*x*sin (x) + 2*x *cos(x)*sin(x)
/ 2 2 / 2 2 \ \ 2*\sin (x) - x *\sin (x) - cos (x)/ + 4*x*cos(x)*sin(x)/
/ / 2 2 \ 2 \ 4*\- 3*x*\sin (x) - cos (x)/ + 3*cos(x)*sin(x) - 2*x *cos(x)*sin(x)/