Misc 22 - Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)
Last updated at Sept. 6, 2021 by Teachoo
Last updated at Sept. 6, 2021 by Teachoo
Transcript
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)
Derivatives by formula - sin & cos
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