A student differentiates as follows: g'(x)=2x x+(x^ 2 +1) x

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

A student differentiates g(x)=(x2+1)tan⁡xg(x)=(x^{2}+1)\tan x as follows: g′(x)=2xtan⁡x+(x2+1)sec⁡x.g'(x)=2x\tan x+(x^{2}+1)\sec x. Answer the following. (i) Identify and explain the error(s) in the student’s working. (ii) Write the correct derivative g′(x)g'(x), giving brief justification for each step.

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