/ 1 \ cos|--------| \log(2*x)/
cos(1/log(2*x))
Let .
The derivative of cosine is negative sine:
Then, apply the chain rule. Multiply by :
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 :
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:
The answer is:
/ 1 \ sin|--------| \log(2*x)/ ------------- 2 x*log (2*x)
/ / 1 \ / 1 \ \ |cos|--------| 2*sin|--------| | | \log(2*x)/ \log(2*x)/ / 1 \| -|------------- + --------------- + sin|--------|| | 2 log(2*x) \log(2*x)/| \ log (2*x) / --------------------------------------------------- 2 2 x *log (2*x)
/ 1 \ / 1 \ / 1 \ / 1 \ / 1 \ sin|--------| 3*cos|--------| 6*sin|--------| 6*cos|--------| 6*sin|--------| / 1 \ \log(2*x)/ \log(2*x)/ \log(2*x)/ \log(2*x)/ \log(2*x)/ 2*sin|--------| - ------------- + --------------- + --------------- + --------------- + --------------- \log(2*x)/ 4 2 log(2*x) 3 2 log (2*x) log (2*x) log (2*x) log (2*x) ------------------------------------------------------------------------------------------------------- 3 2 x *log (2*x)