If for all and

MATHEMATICS · Multi correct · A Level · Mathematics · Differentiation · Differentiation

Problem

If fn(x)=efn−1(x)f_n(x)=e^{f_{n-1}(x)} for all n∈Nn\in\mathbb{N} and f0(x)=xf_0(x)=x, then ddx{fn(x)}\frac{d}{dx}\{f_n(x)\} is (a) fn(x)ddx{fn−1(x)}f_n(x)\frac{d}{dx}\{f_{n-1}(x)\} (b) fn(x)fn−1(x)f_n(x)f_{n-1}(x) (c) fn(x)fn−1(x)⋯f2(x)f1(x)f_n(x)f_{n-1}(x)\cdots f_2(x)f_1(x) (d) None of these

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