Find f′(x)f'(x)f′(x) for f(x)=ex1+x2f(x) = \frac{e^x}{1+x^2}f(x)=1+x2ex using the quotient rule.
ex(1−x2)(1+x2)2\frac{e^x(1-x^2)}{(1+x^2)^2}(1+x2)2ex(1−x2)
ex(x2+2x+1)(1+x2)2\frac{e^x(x^2 + 2x + 1)}{(1+x^2)^2}(1+x2)2ex(x2+2x+1)
ex(x2−2x+1)(1+x2)2\frac{e^x(x^2 - 2x + 1)}{(1+x^2)^2}(1+x2)2ex(x2−2x+1)
ex(x2−2x−1)(1+x2)2\frac{e^x(x^2 - 2x - 1)}{(1+x^2)^2}(1+x2)2ex(x2−2x−1)