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Ex 13.2, 11 - Chapter 13 Class 11 Limits and Derivatives - Part 7

Ex 13.2, 11 - Chapter 13 Class 11 Limits and Derivatives - Part 8
Ex 13.2, 11 - Chapter 13 Class 11 Limits and Derivatives - Part 9

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Ex 13.2, 11 Find the derivative of the following functions: (iv) cosec x Let f (x) = cosec x f(x) = 1/sin⁑π‘₯ Let u = 1 & v = sin x ∴ f(x) = 𝑒/𝑣 So, f’(x) = (𝑒/𝑣)^β€² Using quotient rule f’(x) = (𝑒^β€² 𝑣 βˆ’γ€– 𝑣〗^β€² 𝑒)/𝑣^2 Finding u’ & v’ u = 1 u’ = 0 & v = sin x v’ = cos x Now, f’(x) = (𝑒^β€² 𝑣 βˆ’γ€– 𝑣〗^β€² 𝑒)/𝑣^2 = (0 (sin⁑〖π‘₯) βˆ’γ€– cos〗⁑〖π‘₯ (1)γ€— γ€—)/(〖𝑠𝑖𝑛〗^2 π‘₯) (Derivative of constant function = 0) (Derivative of sin x = cos x) = (0 βˆ’ π‘π‘œπ‘  π‘₯)/(〖𝑠𝑖𝑛〗^2 π‘₯) = (βˆ’ π‘π‘œπ‘  π‘₯)/(〖𝑠𝑖𝑛〗^2 π‘₯) = (βˆ’ π‘π‘œπ‘  π‘₯)/sin⁑π‘₯ . 1/sin⁑π‘₯ = – cot x cosec x = – cosec x cot x Hence f’(x) = – cosec x cot x Using cot x = π‘π‘œπ‘ /sin⁑π‘₯ & 1/sin⁑π‘₯ = cosec x

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.