2 log (cos(2*x))
log(cos(2*x))^2
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
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:
The result of the chain rule is:
Now simplify:
The answer is:
-4*log(cos(2*x))*sin(2*x) ------------------------- cos(2*x)
/ 2 2 \ | sin (2*x) sin (2*x)*log(cos(2*x))| 8*|-log(cos(2*x)) + --------- - -----------------------| | 2 2 | \ cos (2*x) cos (2*x) /
/ 2 2 \ | 3*sin (2*x) 2*sin (2*x)*log(cos(2*x))| 16*|3 - 2*log(cos(2*x)) + ----------- - -------------------------|*sin(2*x) | 2 2 | \ cos (2*x) cos (2*x) / --------------------------------------------------------------------------- cos(2*x)