A student differentiates and writes

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

A student differentiates p(x)=3x−4cos⁡xp(x)=3x-4\cos x and writes p′(x)=3+4sin⁡xp'(x)=3+4\sin x. Which one of the following statements correctly describes the student's result? (a) p′(x)p'(x) should be 3−4sin⁡x3-4\sin x; the student missed the negative sign. (b) The student’s result is correct. (c) p′(x)p'(x) should be 3−4cos⁡x3-4\cos x; the student differentiated cos⁡x\cos x incorrectly. (d) p′(x)p'(x) should be 3x+4sin⁡x3x+4\sin x; the derivative of 3x3x was taken incorrectly.

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