2 2*sin (x)*cos(x)
d / 2 \ --\2*sin (x)*cos(x)/ dx
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the product rule:
; to find :
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of sine is cosine:
The result of the chain rule is:
; to find :
The derivative of cosine is negative sine:
The result is:
So, the result is:
Now simplify:
The answer is:
3 2 - 2*sin (x) + 4*cos (x)*sin(x)
/ 2 2 \ -2*\- 2*cos (x) + 7*sin (x)/*cos(x)
/ 2 2 \ 2*\- 20*cos (x) + 7*sin (x)/*sin(x)