The derivative of cosec x is

Assessment: JAMB UTME - Mathematics - 1995 Subject: General Mathematics

Question 1 Report

The derivative of cosec x is
Answer Details
The derivative of cosec x is -cot x cosec x. Cosec x is the reciprocal of sin x, so we can rewrite it as (1/sin x). Using the quotient rule of differentiation, we can find the derivative of cosec x as follows: d/dx (cosec x) = d/dx (1/sin x) = (-1/sin^2x) * d/dx (sin x) Now, using the chain rule, we can find the derivative of sin x: d/dx (sin x) = cos x Substituting this back into our original expression, we get: d/dx (cosec x) = (-1/sin^2x) * cos x Simplifying this, we get: d/dx (cosec x) = -cot x cosec x

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