Originally Posted by

**hazecraze** **Find f '(x) and f ''(x) of f(x)= (x^2)/(1+4x)**

I found **f'**:

f'= (2x+4x^2)/(1+4x)^2.

**for f"**

[(2+8x)(1+4x)^2 - 2(1+4x)(4)]/[(1+4x)^2]^2

*I know this is correct, but I have to input it in an online grader so it has to be in it's most simplified form.*

so...

factoring a (1+4x)^2=

(1+4x)[(2+8x)(1+4x)-8]/[(1+4x)^4]

(1+4x)[(2+8x+8x+32x^2)-8]/[(1+4x)^4]

(1+4x)[(2+8x+8x+32x^2)-8]/[(1+4x)^4]

(1+4x)[(16x+32x^2-6]/[(1+4x)^4]

factoring out a 2:

(2+8x)[(16x^2+8x-3)]/[(1+4x)^4] *was marked wrong*

Any arithmetic/calculus errors or can it be simplified further?