Help

Before I can try to help you, is the fraction:

(x^2)/(4+x) ("plus x" is part of the denominator)

or

((x^2)/4) + x ("plus x" is not part of the fraction and is a separate term)

"x^2" is a representation of "x squared"

So, as Regina implied above, it's kind of difficult to tell which equation you're talking about. However, I'll just go through both of the possibilities. And, I'm assuming that by double prime, you mean to find the second derivative of the function. 

For f(x) = (x^2)/(4+x)

Using the quotient rule for differentiation, which states that if f(x) = top/bottom, then f'(x) = (top'*bottom - top*bottom') / (bottom^2),

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

       = ((x^2) + 4x) / ((x+4)^2)

and by the same rule, 

f''(x) = [ (2x+4)((x+4)^2) - 2((x^2)+4x)(x+4) ] / ((x+4)^4)

For the other case, where f(x) = (x^2)/4 + x

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

f'(x) = (x/2) + 1

By the power rule in differentiation.

And f''(x) = 1/2

If you still have any questions about the process above, then please do ask!