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

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  1. Chapter 13 Class 11 Limits and Derivatives
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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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