Mathematics

Mathematics

Problem

Which of the following best explains why the derivative of csc⁡x\csc x has a negative sign? a) Because the derivative of sin⁡x\sin x is −cos⁡x-\cos x, so differentiating 1/sin⁡x1/\sin x introduces the negative b) Because csc⁡x\csc x is the reciprocal of sin⁡x\sin x, and differentiating a reciprocal introduces a negative factor c) Because csc⁡x\csc x is an odd function, and differentiating an odd function produces an extra negative sign d) Because csc⁡x\csc x is often confused with sin⁡−1x\sin^{-1}x, whose derivative carries a minus sign

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