3*sin(2*x)*cos(x)
(3*sin(2*x))*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 .
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:
So, the result is:
; to find :
The derivative of cosine is negative sine:
The result is:
Now simplify:
The answer is:
-3*sin(x)*sin(2*x) + 6*cos(x)*cos(2*x)
-3*(4*cos(2*x)*sin(x) + 5*cos(x)*sin(2*x))
3*(-14*cos(x)*cos(2*x) + 13*sin(x)*sin(2*x))