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Misc 24 - Find derivative: (ax2 + sin x) (p + q cos x) - Miscellaneous

Misc 24 - Chapter 13 Class 11 Limits and Derivatives - Part 2

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Misc 24 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): (ax2 + sin x)( p + q cos x) Let f (x) = (ax2 + sin x) (p + q cos x) Let u = ax2 + sin x & v = p + q cos x ∴ f(x) = uv So, f’(x) = (𝑢𝑣)^′ Using product rule = 𝑢^′ 𝑣+〖 𝑣〗^′ 𝑢 Finding u’ & v’ u = ax2 + sin x u’ = (ax2 + sin x)’ = 2ax + cos x v = p + q cos x v’ = (p + q cos x)’ = 0 + q (– sin x) = – q sin x Now, f’(x) = 𝑢^′ 𝑣+〖 𝑣〗^′ 𝑢 = (2ax + cos x) (p + q cos x) + ( – q sin x) (ax2 + sin x) = – q sin x (ax2 + sin x) + (p + q cos x) (2ax + cos x) (xn)’ = n xn – 1 Derivative of sin x = cos x Derivative of cos x = – sin x Derivative of constant = 0

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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.