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# Two easy differentiations watch

1. I am supposed to show whether F’(x) = f(x) or not.

I would be very thankful if someone could check my results in these two assignments.

F(x) = 0,5*ln(e^2x-1), x>0 and f(x) = 1/(e^2x-1),x>0 =>
F’(x) = 0,5*1/(e^2x-1)*e^2x*2 = e^2x/(e^2x-1) =/ (not equal to) f(x).

F(x) = lnlxl and f(x) = 1/x =>
???

Obviously,

lnlxl = lnx for x>0 and lnlxl = ln(-x) for x<0. I just don’t know how to take advantage of this information.
2. The first one is OK. F'(x) ≠ f(x)

In the 2nd one, whether F(x) = ln(x) or F(x) = ln(-x), F'(x) will, in both cases, be F'(x) = 1/x.

So here F'(x) = f(x)

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