2 sin (x)*cos(3*x)
sin(x)^2*cos(3*x)
Apply the product rule:
; to find :
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:
; 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 - 3*sin (x)*sin(3*x) + 2*cos(x)*cos(3*x)*sin(x)
/ / 2 2 \ 2 \ -\2*\sin (x) - cos (x)/*cos(3*x) + 9*sin (x)*cos(3*x) + 12*cos(x)*sin(x)*sin(3*x)/
/ 2 2 \ 2 18*\sin (x) - cos (x)/*sin(3*x) + 27*sin (x)*sin(3*x) - 62*cos(x)*cos(3*x)*sin(x)