2 log (x) - log(log(x))
d / 2 \ --\log (x) - log(log(x))/ dx
Differentiate term by term:
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of is .
The result of the chain rule is:
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
The derivative of is .
Then, apply the chain rule. Multiply by :
The derivative of is .
The result of the chain rule is:
So, the result is:
The result is:
Now simplify:
The answer is:
1 2*log(x) - -------- + -------- x*log(x) x
1 1 2 + ------ + ------- - 2*log(x) log(x) 2 log (x) ------------------------------- 2 x
3 2 2 -6 - ------- - ------ - ------- + 4*log(x) 2 log(x) 3 log (x) log (x) ------------------------------------------ 3 x