Solving y = (3x)^x with the Chain Rule | Homework Help

[moe darklight]

Homework Statement

y = (3x)^x

(find y' )

Homework Equations

y = a^x
y' = (a^x)(ln(a))

and the chain rule

The Attempt at a Solution

3((3x)^x)(ln(3x))

 

[rock.freak667]

Take ln of both sides of the equation

lny=x*ln(3x)

Now use implicit differentiation

 

[moe darklight]

yes, that was the answer that was provided; but I don't understand why my answer is incorrect, given the fact that the derivative of a^x is (a^x)(lin(a)) and the formula seems to be of that form.

 

[rock.freak667]

I believe for that equation to work 'a' must be a constant.

 

[moe darklight]

O, thanks.