Having trouble finding the derivative

[reardear]

\(\displaystyle \large g(x) = \frac{4x-3.8}{(4x-14.44)^2}\)

\(\displaystyle \large g'(x) = \frac{ (4(4x-14.44)^2) - ((4x-3.8)(2)(4x-14.44)(4)) }{(4x-14.44)^4}\)

\(\displaystyle \large g'(x) = \frac{ (64x^2 -462.08x + 834.054) - (32x^2 + 145.92x - 109.744) }{(4x-14.44)^4}\)

\(\displaystyle \large g'(x) = \frac{ 32x^2 - 316.16x + 724.31 }{(4x-14.44)^4}\)

I can't seem to arrive at the correct answer and I'm not sure why and where I'm doing it wrong. That's one of the multiple attempts I've done.

 

[daon2]

Your derivative (on the first line) is correct. So the problem is the simplification then?

Instead of multiplying everything out, notice you can factor out 4(4x-14.44) from the numerator. Then one of the (4x-14.44)'s in the denominator will cancel with this one.

Finally you are left with simplifying 4[(4x-14.44)-2(4x-3.8)] / (4x-14.4)³, a much easier task.

So, before multiplying everything (!) factor first!