sin(4*x)*cos(2*x)
sin(4*x)*cos(2*x)
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 :
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*sin(2*x)*sin(4*x) + 4*cos(2*x)*cos(4*x)
-4*(4*cos(4*x)*sin(2*x) + 5*cos(2*x)*sin(4*x))
8*(-14*cos(2*x)*cos(4*x) + 13*sin(2*x)*sin(4*x))