2 log (2*x - 1)
d / 2 \ --\log (2*x - 1)/ dx
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 :
Differentiate term by term:
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 derivative of the constant is zero.
The result is:
The result of the chain rule is:
The result of the chain rule is:
Now simplify:
The answer is:
4*log(2*x - 1) -------------- 2*x - 1
8*(1 - log(-1 + 2*x)) --------------------- 2 (-1 + 2*x)
16*(-3 + 2*log(-1 + 2*x)) ------------------------- 3 (-1 + 2*x)