2 sin (cos(3*x)) + 2*pi
sin(cos(3*x))^2 + 2*pi
Differentiate term by term:
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Let .
The derivative of sine is cosine:
Then, apply the chain rule. Multiply by :
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 of the chain rule is:
The result of the chain rule is:
The derivative of the constant is zero.
The result is:
Now simplify:
The answer is:
-6*cos(cos(3*x))*sin(3*x)*sin(cos(3*x))
/ 2 2 2 2 \ 18*\cos (cos(3*x))*sin (3*x) - sin (3*x)*sin (cos(3*x)) - cos(3*x)*cos(cos(3*x))*sin(cos(3*x))/
/ 2 2 2 \ 54*\cos(cos(3*x))*sin(cos(3*x)) - 3*sin (cos(3*x))*cos(3*x) + 3*cos (cos(3*x))*cos(3*x) + 4*sin (3*x)*cos(cos(3*x))*sin(cos(3*x))/*sin(3*x)