Apply the product rule:
; to find :
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:
; 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*x*cos(9*x) + 9*x *sin(9*x)
2 -2*cos(9*x) + 36*x*sin(9*x) + 81*x *cos(9*x)
/ 2 \ 27*\2*sin(9*x) - 27*x *sin(9*x) + 18*x*cos(9*x)/