Apply the product rule:
; to find :
Apply the power rule: goes to
; to find :
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:
The result is:
Now simplify:
The answer is:
3 2 / 2 \ tan (x) + x*tan (x)*\3 + 3*tan (x)/
/ 2 \ / / 2 \ \ 6*\1 + tan (x)/*\x*\1 + 2*tan (x)/ + tan(x)/*tan(x)
/ / 2 \ \ / 2 \ | |/ 2 \ 4 2 / 2 \| / 2 \ | 6*\1 + tan (x)/*\x*\\1 + tan (x)/ + 2*tan (x) + 7*tan (x)*\1 + tan (x)// + 3*\1 + 2*tan (x)/*tan(x)/