Apply the product rule:
; to find :
Apply the power rule: goes to
; 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 - 2*t *sin(2*t) + 2*t*cos(2*t)
/ 2 \ 2*\-4*t*sin(2*t) - 2*t *cos(2*t) + cos(2*t)/
/ 2 \ 4*\-3*sin(2*t) - 6*t*cos(2*t) + 2*t *sin(2*t)/