I've been taught that with the basic form of a function's maclaurin series, complex forms of the same series can be found. For example, the first three terms for arctan(x) are x-x^3/3 + x^5/5, meaning the first three terms for arctan(x^2+1) at a=0 should be (x^2+1) - ((x^2+1)^3)/3 + ((x^2+1)^5/5). If this is the case, why is it?(adsbygoogle = window.adsbygoogle || []).push({});

I can understand why the taylor series for e^2x and other, repetitive functions follow this simple substitution.

But for those functions whose derivatives require repeated application of the chain rule, why does " simple substitution" work.

Thanks

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# Simple Substitution Taylor Polynomials

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