4*sin(x)*cos(x)
d --(4*sin(x)*cos(x)) dx
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the product rule:
; to find :
The derivative of cosine is negative sine:
; to find :
The derivative of sine is cosine:
The result is:
So, the result is:
Now simplify:
The answer is:
2 2 - 4*sin (x) + 4*cos (x)
/ 2 2 \ 16*\sin (x) - cos (x)/