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Misc 27 - Find derivative: x2 cos pi/4 / sin x - Class 11

Misc 27 - Chapter 13 Class 11 Limits and Derivatives - Part 2
Misc 27 - Chapter 13 Class 11 Limits and Derivatives - Part 3

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Misc 27 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): (x2 〖cos 〗⁡〖π/4〗)/sin⁡x Let f (x) = (𝑥2 〖cos 〗⁡〖𝜋/4〗)/(sin x) Let u = x2 cos 𝜋/4 & v = sin x So, f(x) = 𝑢/𝑣 ∴ f’(x) = (𝑢/𝑣)^′ Using quotient rule f’(x) = (𝑢^′ 𝑣 −〖 𝑣〗^′ 𝑢)/𝑣^2 Finding u’ & v’ u = x2 cos 𝜋/4 u’ = 2x cos 𝜋/4 & v = sin x v’= cos x Now, f’(x) = (𝑢/𝑣)^′ = (𝑢^′ 𝑣 −〖 𝑣〗^′ 𝑢)/𝑣^2 Derivative of xn is nxn – 1 & cos 𝜋/4 is constant (Derivative of sin x = cos x) = (2𝑥 cos⁡〖𝜋/4〗 (sin⁡〖𝑥)〗 −(cos⁡〖𝑥) (𝑥^2 cos⁡〖𝜋/4) 〗 〗)/(〖𝑠𝑖𝑛〗^2 𝑥) = (2𝑥 〖𝑠𝑖𝑛 𝑥 cos 〗⁡〖𝜋/4〗 − 𝑥^2 cos⁡〖𝑥 .〖cos 〗⁡〖𝜋/4〗 〗)/(〖𝑠𝑖𝑛〗^2 𝑥) = (𝒙 〖𝐜𝐨𝐬 〗⁡〖𝝅/𝟒〗 (𝟐 𝐬𝐢𝐧⁡〖𝒙 − 𝒙 𝐜𝐨𝐬⁡〖𝒙) 〗 〗)/(〖𝒔𝒊𝒏〗^𝟐 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.