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Misc 15 - Find derivative: cosec x cot x - Chapter 13 Limits - Derivatives by formula - other trignometric

Misc 15 - Chapter 13 Class 11 Limits and Derivatives - Part 2

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Misc 15 Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): cosec x cot x Let f(x) = cosec x cot x Let u = cosec x & v = cot x So, f(x) = uv f (x) = (uv) Using product rule f (x) = u v + v u Finding u & v u = cosec x u = cosec x cot x v = cot x v = cosec2x Now, f (x) = (uv) = u v + v u = cosec x cot x (cot x) + ( cosec2x) (cosec x) = cosec x . cot2 x cosec3x = cosec3x cosec x cot2x

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