Question

Evaluate ^d⁄dx Cot(x)Cosec(x)

(a) -Cosec^2 (x) – Cosec^2 (x)Cot(x)

(b) -Cosec^3 (x) – Cosec^2 (x)Cot(x)

(c) -Cosec(x) – Cosec^2 (x)Cot(x)

(d) -Cosec^3 (x) – Cosec(x)Cot^2 (x)

The question was posed to me in an interview.

The above asked question is from Limits and Derivatives of Several Variables in portion Partial Differentiation of Engineering Mathematics

Answer 1

The correct option is (b) -Cosec^3 (x) – Cosec^2 (x)Cot(x)

Best explanation: ^d⁄dx Cot(x)Cosec(x) = -Cosec^3 (x) – Cosec^2 (x)Cot(x).(By multiplication rule)