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I asked this question a couple of days ago, and I have been working on it a lot since then. Please see if you know what I can do next

Here is the question:

Suppose a computer program is available which yields values for arcsin y in floating point representation with t decimal mantissa places and for |y|<=1 subject to a relative error eps with |eps|<=10exp-t. In view of the relation

arctan x = arcsin [x/(sqrt(1+x^2)]

this program could also be used to evaluate arctan x. Determine for which values x this procedure is numerically stable by estimating the relative error.

I have calculated the relative error by taking the derivative of the RHS and multiplying that by x/arctan x, which is the realtive error equation, but it makes no sense to me. What do I do with it now? I got

relative error = (x^3/arctanx)[(1+x^2)^3/2 + (1+x^2)^1/2]*(epsilon of x)

Thanks for any input,

CC