[微分] 證明題

[torrap (對自己好才是好^.^)]

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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