Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Rewrite the function to be differentiated:
Apply the quotient rule, which is:
and .
To find :
The derivative of sine is cosine:
To find :
The derivative of cosine is negative sine:
Now plug in to the quotient rule:
The result of the chain rule is:
Now simplify:
The answer is:
2 -1 - tan (x) ------------ 2 tan (x)
/ 2 \ / 2 \ | 1 + tan (x)| 2*\1 + tan (x)/*|-1 + -----------| | 2 | \ tan (x) / ---------------------------------- tan(x)
/ 3 2\ | / 2 \ / 2 \ | | 2 3*\1 + tan (x)/ 5*\1 + tan (x)/ | 2*|-2 - 2*tan (x) - ---------------- + ----------------| | 4 2 | \ tan (x) tan (x) /