log(cos(2*x))
d --(log(cos(2*x))) dx
Let .
The derivative of is .
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:
Now simplify:
The answer is:
-2*sin(2*x) ----------- cos(2*x)
/ 2 \ | sin (2*x)| -4*|1 + ---------| | 2 | \ cos (2*x)/
/ 2 \ | sin (2*x)| -16*|1 + ---------|*sin(2*x) | 2 | \ cos (2*x)/ ---------------------------- cos(2*x)