Derivative Problem involving Natural Log

[SMA83]

Homework Statement

Evaluate the derivative of the following function:

p(x) = (5x)^-ln(5x)

Homework Equations

\frac{d}{dx}lnx = \frac{1}{x}
Not sure what else...

The Attempt at a Solution

I know that I will have to use the chain rule in this problem, but actually implementing it is giving me problems. I wish I could give more of an attempt, but I don't really even know where to start. Thanks in advance for the help!

 

[eczeno]

have you heard of the technique 'logarithmic differentiation'? it is where you take the log on both sides and then differentiate implicitly.

 

[vela]

You could also use the fact that a^b is defined as e^{b log a}.