d/dx (f(x)/g(x))
= lim[h→0]((f(x+h)/g(x+h) - f(x)/g(x) )/ h )
= lim[h→0]((f(x+h) g(x) - f(x) g(x+h) )/(h g(x+h) g(x)))
= lim[h→0]((f(x+h) g(x) - f(x) g(x) - f(x) g(x+h) + f(x) g(x) )/(h g(x+h) g(x)))
= lim[h→0]((( f(x+h) - f(x)) g(x) - f(x) ( g(x+h) - g(x)) )/(h g(x+h) g(x)))
= lim[h→0]((((f(x+h) - f(x))/h) g(x) - f(x) ((g(x+h) - g(x))/h))/(g(x+h) g(x)))
= ( f'(x) g(x) - f(x) g'(x) )/(g(x+0) g(x))
= ( f'(x) g(x) - f(x) g'(x) )/(g(x))^2
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