sin(3*x)*cos(x)
d --(sin(3*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 :
The derivative of cosine is negative sine:
The result is:
Now simplify:
The answer is:
-sin(x)*sin(3*x) + 3*cos(x)*cos(3*x)
-2*(3*cos(3*x)*sin(x) + 5*cos(x)*sin(3*x))
4*(-9*cos(x)*cos(3*x) + 7*sin(x)*sin(3*x))