2 log (3*x - 2)
d / 2 \ --\log (3*x - 2)/ 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:
6*log(3*x - 2) -------------- 3*x - 2
18*(1 - log(-2 + 3*x)) ---------------------- 2 (-2 + 3*x)
54*(-3 + 2*log(-2 + 3*x)) ------------------------- 3 (-2 + 3*x)