

Last updated at March 9, 2017 by Teachoo
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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 π4 sinx Let f (x) = 𝑥2 cos 𝜋4sin x Let u = x2 cos 𝜋4 & v = sin x So, f(x) = 𝑢𝑣 ∴ f’(x) = 𝑢𝑣′ Using quotient rule f’(x) = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 Finding u’ & v’ u = x2 cos 𝜋4 u’ = 2x2 –1 cos 𝜋4 = 2x cos 𝜋4 & v = sin x v’= cos x Now, f’(x) = 𝑢𝑣′ = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 = 2𝑥 cos 𝜋4 ( sin𝑥) −( cos𝑥) ( 𝑥2 cos 𝜋4) 𝑠𝑖𝑛2 𝑥 = 2𝑥 𝑠𝑖𝑛 𝑥 cos 𝜋4 − 𝑥2 cos𝑥 . cos 𝜋4 𝑠𝑖𝑛2 𝑥 = 𝒙 𝐜𝐨𝐬 𝝅𝟒 (𝟐 𝐬𝐢𝐧𝒙 − 𝒙 𝐜𝐨𝐬𝒙) 𝒔𝒊𝒏𝟐 𝒙
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