Apply the quotient rule, which is:
and .
To find :
Apply the product rule:
; to find :
Apply the power rule: goes to
; to find :
There are multiple ways to do this derivative.
Rewrite the function to be differentiated:
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:
Rewrite the function to be differentiated:
Apply the quotient rule, which is:
and .
To find :
The derivative of cosine is negative sine:
To find :
The derivative of sine is cosine:
Now plug in to the quotient rule:
The result is:
To find :
The derivative of the constant is zero.
Now plug in to the quotient rule:
Now simplify:
The answer is:
/ 2 \ | 1 cot (x)| cot(x) x*|- - - -------| + ------ \ 2 2 / 2
2 / 2 \ -1 - cot (x) + x*\1 + cot (x)/*cot(x)