/ / 3\\ log\cos\x //
d / / / 3\\\ --\log\cos\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 :
Apply the power rule: goes to
The result of the chain rule is:
The result of the chain rule is:
Now simplify:
The answer is:
2 / 3\ -3*x *sin\x / ------------- / 3\ cos\x /
/ / 3\ 3 2/ 3\\ | 3 2*sin\x / 3*x *sin \x /| -3*x*|3*x + --------- + -------------| | / 3\ 2/ 3\ | \ cos\x / cos \x / /
/ / 3\ 3 2/ 3\ 6 / 3\ 6 3/ 3\\ | 3 sin\x / 9*x *sin \x / 9*x *sin\x / 9*x *sin \x /| -6*|9*x + ------- + ------------- + ------------ + -------------| | / 3\ 2/ 3\ / 3\ 3/ 3\ | \ cos\x / cos \x / cos\x / cos \x / /