Don't know the steps in finding this derivative.
But the derivative is
Now simplify:
The answer is:
2 x*sin (x) --------- / 2 \ 2 |sin (x) / 2 \ / ___\| x *|------- + \sin (x) + 2*x*cos(x)*sin(x)/*log\\/ x /| \ 2 /
2 x*sin (x) --------- / 2 / / ___\ \\ 2 | / 2 2 \ / ___\ (2*x*cos(x) + sin(x))*sin(x) sin (x)*((2*x*cos(x) + sin(x))*log(x) + sin(x))*\2*(2*x*cos(x) + sin(x))*log\\/ x / + sin(x)/| x *|cos(x)*sin(x) + 2*\x*cos (x) - x*sin (x) + 2*cos(x)*sin(x)/*log\\/ x / + ---------------------------- + ---------------------------------------------------------------------------------------------| \ 2*x 4 /
2 x*sin (x) / / / 2 2 \ / ___\ (2*x*cos(x) + sin(x))*sin(x)\ / / ___\ \ / / 2 2 \ (2*x*cos(x) + sin(x))*sin(x)\ \ --------- | / 2 2 \ ((2*x*cos(x) + sin(x))*log(x) + sin(x))*|2*cos(x)*sin(x) + 4*\x*cos (x) - x*sin (x) + 2*cos(x)*sin(x)/*log\\/ x / + ----------------------------|*sin(x) \2*(2*x*cos(x) + sin(x))*log\\/ x / + sin(x)/*|2*\x*cos (x) - x*sin (x) + 2*cos(x)*sin(x)/*log(x) + 2*cos(x)*sin(x) + ----------------------------|*sin(x) 2 3 / / ___\ \| 2 | 2 2 / 2 2 \ / ___\ 2*\x*cos (x) - x*sin (x) + 2*cos(x)*sin(x)/ \ x / (2*x*cos(x) + sin(x))*sin(x) \ x / ((2*x*cos(x) + sin(x))*log(x) + sin(x)) *sin (x)*\2*(2*x*cos(x) + sin(x))*log\\/ x / + sin(x)/| x *|cos (x) - sin (x) - 2*\- 3*cos (x) + 3*sin (x) + 4*x*cos(x)*sin(x)/*log\\/ x / + ------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------| | x 2 2 4 8 | \ 2*x /