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

Use the quotient and product rules to solve.

f(x) = x²/(4+x)
f'(x) = [2x(4+x) - x²] / (4+x)²
f'(x) = (8x + 2x² - x²) / (x² + 8x + 16)
f'(x) = (x² + 8x) / (x² + 8x + 16)
f''(x) = [(2x+8)(x²+8x+16) - (2x+8)(x²+8x)] / (x²+8x+16)²
f''(x) = (2x+8)[(x²+8x+16) - (x²+8x)] / (x²+8x+16)²
f''(x) = 16(2x+8) / [(x+4)²]²
f''(x) = 16*2(x+4) / (x+4)^4
f''(x) = 32 / (x+4)^3
f''(2) = 32 / (2 + 4)^3
f''(2) = 32 / 6^3
f''(2) = 32 / 216
f''(2) = 4/27

Hope that helps :)