2 -log(2)*cos (log(x))
d / 2 \ --\-log(2)*cos (log(x))/ dx
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
Apply the power rule: goes to
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 is .
The result of the chain rule is:
The result of the chain rule is:
So, the result is:
Now simplify:
The answer is:
2*cos(log(x))*log(2)*sin(log(x)) -------------------------------- x
/ 2 2 \ -2*\sin (log(x)) - cos (log(x)) + cos(log(x))*sin(log(x))/*log(2) ----------------------------------------------------------------- 2 x
/ 2 2 \ -2*\- 3*sin (log(x)) + 3*cos (log(x)) + 2*cos(log(x))*sin(log(x))/*log(2) ------------------------------------------------------------------------- 3 x