一个简单导数公式应该怎么样推导,如f(x)/g(x)

楼上都答非所问,问的是「推导过程」,可从定义出发.
导数的商公式证明：
设有函数u = f(x)及v = g(x)
(u/v)' = d/dx [f(x)/g(x)] = lim(Δx→0) Δy/Δx
= lim(Δx→0) [f(x + Δx)/g(x + Δx) - f(x)/g(x)]/Δx
= lim(Δx→0) 1/[g(x + h)g(x)] • lim(Δx→0) [f(x + Δx)g(x) - f(x)g(x + Δx)]/Δx
= 1/[g(x + 0)g(x)] • lim(Δx→0) {[f(x + Δx)g(x) - f(x)g(x)] - [f(x)g(x + Δx) - f(x)g(x)]}/Δx,加减f(x)g(x)
= 1/[g(x)]² • lim(Δx→0) {[f(x + Δx)g(x) - f(x)g(x)]/Δx - [f(x)g(x + Δx) - f(x)g(x)]/Δx}
= 1/[g(x)]² • {g(x) • lim(Δx→0) [f(x + Δx) - f(x)]/Δx - f(x) • lim(Δx→0) [g(x + Δx) - g(x)]/Δx}
= 1/[g(x)]² • [g(x) • d/dx f(x) - f(x) • d/dx g(x)]
= [g(x)f'(x) - f(x)g'(x)]/[g(x)]²
= (vu' - uv')/v²