Deriving Radicals: Tips for Finding the Correct Derivative - Physics Problem

[Lemniscate]

Homework Statement

It's been a while since I've done derivatives. I'm working on a physics problem and can't seem to get the correct derivate for a function of the following form:

f(x)= A [1+9x^2(x-4)^2]^1/2

A is a constant.

The Attempt at a Solution

I've tried various ways of deriving. Silly. But nothing works for the physics problem I am working with.
I derived the whole radical. Brought down the 1/2 and was left with the what's inside the radical raised to -1/2 and then deriving the inside.

I believe my final derivative is in terms of A and x.

Any tips on how to derive this function?

 

[rock.freak667]

expand 9x²(x-4)², then differentiate the inside of the radical.

though I am not sure why you need help if you said you did it already as you did the correct steps.

 

[Lemniscate]

Hm. I believe I am doing the derivative correctly.

This is what I get:
A*(36t^3-216t^2+288t) all over 2*(9t^4-72t^3+144t^2+1)^1/2

However, I am trying to enter the acquired derivative into a program I'm using for Physics and the deriv I entered (the one above) is "not correct."
Can someone let me know if the deriv is correct or not? Because if it is, then I'm doing something wrong when entering my answer... then that would be a whole other story.

 

[Lemniscate]

Problem solved!
Silly mistake I made while submitting my correct derivative.
Thanks for your help though. Expanding the product made things easier.