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:
5 / 2 \ tan (x)*\6 + 6*tan (x)/
4 / 2 \ / 2 \ 6*tan (x)*\1 + tan (x)/*\5 + 7*tan (x)/
/ 2 \ 3 / 2 \ | 4 / 2 \ 2 / 2 \| 24*tan (x)*\1 + tan (x)/*\tan (x) + 5*\1 + tan (x)/ + 8*tan (x)*\1 + tan (x)//