A function f(x)f(x)f(x) is defined such that f′(x)=f(x)2f'(x) = f(x)^2f′(x)=f(x)2 and f(0)=1f(0) = 1f(0)=1. Find f(x)f(x)f(x).
f(x)=11−xf(x) = \frac{1}{1-x}f(x)=1−x1
f(x)=exf(x) = e^xf(x)=ex
f(x)=11+xf(x) = \frac{1}{1+x}f(x)=1+x1
f(x)=tan(x)+1f(x) = \tan(x) + 1f(x)=tan(x)+1