Differentiation of a function of discrete variable

kindlychung

例题中微分的用法让人不解。
另外，n=1为什么会变成n=0呢？

elimqiu

(d/dq)q^n = nq^(n-1) 总是是成立的
幂级数在收敛开区间内是可以逐项微分的。利用求和与微分的这种可交换性，得到幂级数的初等函数表达。这是一种常用的技巧。
n起始于1 改为 起始于 0 不会改变计算结果，却简化了计算。

kindlychung

Derivative a function of a real variable is defined to be the rate of change when the change of both independent and dependent variables are infinitesimal.
In the case of q^n, n cannot be infinitesimal, I think d/dq must be defined differently, how is it defined?

elimqiu

Here you just view q^n as the nth power of continuous variable q

kindlychung

Alright. I still don';t get, but I';ll leave it for later review.
Thank you.