Derivative of exponential function

[cal.queen92]

Homework Statement

I am trying the find the derivative of the function:

y= (2x-1)^(tan(3x))

Homework Equations

Chain rule, in this case: f'(g(h(x))) * g'(h(x)) * h'(x)

exponent rule: where (d/dx) a^x = (a^x) ln a

The Attempt at a Solution

I feel as if to apply the chain rule, I need to separate the function into three functions:

f(x) = (2x-1)^x g(x) = tanx h(x) = 3x

However, from here, I am not sure how to differentiate (2x-1)^x

How can I apply the exponent rule to this function?

Any ideas?
Thanks!

 

[hotvette]

Try taking the natural log of both sides of y = (2x-1)^(tan(3x)) and performing implicit differentiation.

 

[cal.queen92]

Thank you!