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DCC Bridge
Anonymous1782404023
06-25 16:15
Model Name
human figure 3d model
Tags
character
rendering
realistic
Prompt
I want a detailed video lesson that shows, from first principles, how to differentiate f(x) = e^{arctan x} using the limit definition. Walk through every algebraic step: substitute y = arctan x and k = arctan(x+h) - arctan x, rewrite the limit in k, factor and expand e^{y+k}-e^y using the Taylor series for e^k, simplify tan(y+k)-tan y into sin k/(cos(y+k)cos y) using trig identities, isolate the standard limit k/sin k, evaluate all limits and then convert back to x to obtain e^{arctan x}/(1+x^2). Explain and justify each identity and standard limit used, give the geometric/intuitive reasons for the substitution, and go line-by-line through the scanned solution image shown in the chat, pointing out why each manipulation is valid.
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