2 3*sin (x)*cos(x)
(3*sin(x)^2)*cos(x)
Apply the product rule:
; to find :
The derivative of a constant times a function is the constant times the derivative of the function.
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:
So, the result is:
; to find :
The derivative of cosine is negative sine:
The result is:
Now simplify:
The answer is:
3 2 - 3*sin (x) + 6*cos (x)*sin(x)
/ 2 2 \ -3*\- 2*cos (x) + 7*sin (x)/*cos(x)