Misc 22 - Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)
Last updated at Sept. 6, 2021 by Teachoo
Miscellaneous (Term 1 and Term 2)
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Misc 22 Important You are here
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Miscellaneous (Term 1 and Term 2)
Last updated at Sept. 6, 2021 by Teachoo
Misc 22 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): x4 (5 sin x – 3 cos x) Let f (x) = x4 (5 sin x – 3 cos x) Let u = x4 & v = 5 sin x – 3 cos x ∴ f(x) = uv So, f’(x) = 𝑢𝑣′ f’(x) = 𝑢′𝑣 − 𝑣′𝑢 Finding u’ & v’ u = x4 u’ = 4x4 – 1 = 4x3 & v = 5 sin x – 3 cos x v’ = 5(sin x)’ – (3 cos x)’ v’ = 5 cos x – 3 ( – sin x) = 5 cos x + 3 sin x Now, f’(x) = 𝑢𝑣′ = 𝑢′𝑣 − 𝑣′𝑢 = 4x3 (5 sin x – 3 cos x) + (5 cos x + 2sin x) (x4) = x3 (4 (5 sin x – 3cos x) + x (5 cos x + 3 sin x)) = x3 (20 sin x – 12 cos x + 5x . cos x + 3 . sin x) = x3 (5x cos x + 3x sin x + 20 sin x – 12 cos x)