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Misc 23 - Find derivative: (x2 + 1) cos x - Class 11 NCERT - Derivatives by formula - sin & cos

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  1. Chapter 13 Class 11 Limits and Derivatives
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Misc 23 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 + 1) cos x Let f (x) = (x2 + 1) cos x Let u = (x2 + 1) & v = cos x ∴ f(x) = uv So, f’(x) = 𝑢𝑣﷯﷮′﷯ Using product rule f’(x) = 𝑢﷮′﷯𝑣+ 𝑣﷮′﷯𝑢 Finding u’ & v’ u = x2 + 1 u’ = 2. x2 –1 + 0 = 2x & v = cos x v’= – sin x Now, f’(x) = 𝑢𝑣﷯′ = 𝑢﷮′﷯𝑣+ 𝑣﷮′﷯𝑢 = 2x ( cos x) + ( – sin x) (x2 + 1) = 2x cos x – sin x (x2 + 1) = 2x cos – x2 sin x – sin x = – x2 sin x – sin x + 2x cos x

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