sin(x) ------ 2 x
d /sin(x)\ --|------| dx| 2 | \ x /
Apply the quotient rule, which is:
and .
To find :
The derivative of sine is cosine:
To find :
Apply the power rule: goes to
Now plug in to the quotient rule:
Now simplify:
The answer is:
cos(x) 2*sin(x) ------ - -------- 2 3 x x
4*cos(x) 6*sin(x) -sin(x) - -------- + -------- x 2 x ----------------------------- 2 x
24*sin(x) 6*sin(x) 18*cos(x) -cos(x) - --------- + -------- + --------- 3 x 2 x x ------------------------------------------ 2 x