/x\ /x\ sin|-|*cos|-| \2/ \2/
sin(x/2)*cos(x/2)
Apply the product rule:
; to find :
Let .
The derivative of sine is cosine:
Then, apply the chain rule. Multiply by :
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
The result of the chain rule is:
; to find :
Let .
The derivative of cosine is negative sine:
Then, apply the chain rule. Multiply by :
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
The result of the chain rule is:
The result is:
Now simplify:
The answer is:
2/x\ 2/x\ cos |-| sin |-| \2/ \2/ ------- - ------- 2 2
/x\ /x\ -cos|-|*sin|-| \2/ \2/