A student tries to differentiate and writes the following result:

MATHEMATICS · Multi-part · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

A student tries to differentiate p(x)=7x3−4cos⁡x+5p(x)=7x^3-4\cos x+5 and writes the following result: p′(x)=21x2−4sin⁡x+5\displaystyle p'(x)=21x^2-4\sin x+5. Study the work and answer the following: (i) Copy the student’s derivative and identify the specific term(s) where an error has been made. Give a brief explanation of the mistake. (ii) Determine the correct derivative p′(x)p'(x). (iii) Verify your result by evaluating the correct derivative at x=π3x=\dfrac{\pi}{3}. Give the exact value.

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