Calculate f′(x)f'(x)f′(x) for f(x)=x2x+1f(x) = \frac{x^2}{x + 1}f(x)=x+1x2 using the quotient rule.
x2+2x(x+1)2\frac{x^2 + 2x}{(x + 1)^2}(x+1)2x2+2x
x2−2x(x+1)2\frac{x^2 - 2x}{(x + 1)^2}(x+1)2x2−2x
x2+2xx+1\frac{x^2 + 2x}{x+1}x+1x2+2x
2x(x+1)2\frac{2x}{(x + 1)^2}(x+1)22x