2 sin(2*x)*cos (x)
d / 2 \ --\sin(2*x)*cos (x)/ dx
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 .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of cosine is negative sine:
The result of the chain rule is:
The result is:
Now simplify:
The answer is:
2 2*cos (x)*cos(2*x) - 2*cos(x)*sin(x)*sin(2*x)
// 2 2 \ 2 \ 2*\\sin (x) - cos (x)/*sin(2*x) - 2*cos (x)*sin(2*x) - 4*cos(x)*cos(2*x)*sin(x)/
/ 2 / 2 2 \ \ 4*\- 2*cos (x)*cos(2*x) + 3*\sin (x) - cos (x)/*cos(2*x) + 8*cos(x)*sin(x)*sin(2*x)/