[微分] 證明題
題目是
Suppose that f is a differentiable function
(a) Find d/dx f(f(x))
(b) Find d/dx f(f(f(x)))
(c) Find d/dx f(f(f(f(x)))
(d) Let f[n] denote the function defined as follows:f[1]=f and
f[n]=f。f[n-1] for n>=2.Thus,f[2]=f。f,f[3]=f。f。f, and so
on.Based on your results from parts (a) through (c),make a
conjecture regarding d/dx f[n](x). Prove your conjecture.
^^^^^^^^^^^^^^^^^^^^^^^^
(a)(b)(c)(d)都可以用Chain Rule算出來，
可是最後的證明要如何證明呢?
麻煩知道的大大解一下，謝謝!
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