application of derivative

1. A function f(x) is defined so that for all real x {f(x)}ⁿ = f(nx). Prove that
f(x).f'(nx) = f'(x).f(nx).

2 Answers

n. [ f(x)] ^n-1.f'(x) = n.f'(nx)

[f(x)]ⁿ.[f(x)]^-1 .f'(x) = f'(nx)

[f(x)]ⁿ .f'(x) = f'(nx).f(x) -------1

now

from ques

[f(x)]ⁿ = f(nx)

therefore from ----1

f(nx).f'(x) = f'(nx).f(x)

thanks .i was confused as i take f(x) = e^nx

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