Don't know the steps in finding this derivative.
But the derivative is
The answer is:
acos(2*x) / 2*log(sin(x)) acos(2*x)*cos(x)\ sin (x)*|- ------------- + ----------------| | __________ sin(x) | | / 2 | \ \/ 1 - 4*x /
/ 2 2 \ acos(2*x) |/ 2*log(sin(x)) acos(2*x)*cos(x)\ cos (x)*acos(2*x) 8*x*log(sin(x)) 4*cos(x) | sin (x)*||- ------------- + ----------------| - acos(2*x) - ----------------- - --------------- - --------------------| || __________ sin(x) | 2 3/2 __________ | || / 2 | sin (x) / 2\ / 2 | \\ \/ 1 - 4*x / \1 - 4*x / \/ 1 - 4*x *sin(x)/
/ 3 / 2 \ 2 3 2 \ acos(2*x) |/ 2*log(sin(x)) acos(2*x)*cos(x)\ 6 8*log(sin(x)) / 2*log(sin(x)) acos(2*x)*cos(x)\ |cos (x)*acos(2*x) 4*cos(x) 8*x*log(sin(x)) | 96*x *log(sin(x)) 2*cos (x)*acos(2*x) 2*acos(2*x)*cos(x) 6*cos (x) 24*x*cos(x) | sin (x)*||- ------------- + ----------------| + ------------- - ------------- - 3*|- ------------- + ----------------|*|----------------- + -------------------- + --------------- + acos(2*x)| - ----------------- + ------------------- + ------------------ + --------------------- - --------------------| || __________ sin(x) | __________ 3/2 | __________ sin(x) | | 2 __________ 3/2 | 5/2 3 sin(x) __________ 3/2 | || / 2 | / 2 / 2\ | / 2 | | sin (x) / 2 / 2\ | / 2\ sin (x) / 2 2 / 2\ | \\ \/ 1 - 4*x / \/ 1 - 4*x \1 - 4*x / \ \/ 1 - 4*x / \ \/ 1 - 4*x *sin(x) \1 - 4*x / / \1 - 4*x / \/ 1 - 4*x *sin (x) \1 - 4*x / *sin(x)/