Misc 26 - Chapter 13 Class 11 Limits and Derivatives (Term 1 and Term 2)
Last updated at Dec. 8, 2016 by Teachoo
Last updated at Dec. 8, 2016 by Teachoo
Transcript
Misc 26 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): 4x + 5 sinx3x + 7 cosx Let f (x) = 4𝑥 + 5 sin𝑥3x + 7 cos x Let u = 4x + 5 sin & v = 3x + 7 cos x ∴ f(x) = 𝑢𝑣 So, f’ (x) = 𝑢𝑣′ Using quotient rule f’(x) = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 Finding u’ & v’ u = 4x + 5sin x u’ = (4x + 5sin x)’ = 4 .1 x1 – 1 + 5 cos x = 4 + 5 cos x & v = 3x + 7 cos x v’ = (3x + 7 cos x)’ = 3 . 1x1 – 1 + 7 ( – sin x) = 3x0 + 7 ( – sin x) = 3 – 7 sin x Now, f’(x) = 𝑢𝑣′ = 𝑢′𝑣 − 𝑣′𝑢 𝑣2 = (4 + 5 cos𝑥) (3𝑥 + 7 cos𝑥) − (3 − 7 sin𝑥) (4𝑥 + 5 sin𝑥) (3𝑥 + 7 cos𝑥)2 = 4(3𝑥 + 7 cos𝑥)+5 cos𝑥(3𝑥+7 cos𝑥)−3(4𝑥+5 sin𝑥)+7 sin𝑥 (4𝑥+5 sin𝑥) (3𝑥 + 7 cos𝑥)2 = 12𝑥 + 28 cos𝑥 + 15 cos𝑥 + 35 cos2𝑥 −12𝑥 −15 sin𝑥 +28𝑥 sin𝑥 +35𝑠𝑖𝑛2 𝑥 (3𝑥 + 7 cos𝑥)2 = 28 cos𝑥 + 28𝑥 sin𝑥 + 15 𝑥 cos− 15 sin𝑥 + 35 𝑐𝑜𝑠2 𝑥 + 35 𝑠𝑖𝑛2 𝑥 (3𝑥 + 7 cos𝑥)2 = 28( cos𝑥 + 𝑥 sin𝑥) + 15(𝑥 cos𝑥 − sin𝑥) + 35 (𝒔𝒊𝒏𝟐𝒙 + 𝒄𝒐𝒔𝟐 𝒙) (3𝑥 + 7 cos𝑥)2 = 28( cos𝑥 + 𝑥 sin𝑥) + 15(𝑥 cos𝑥 − sin𝑥) + 35 𝟏 (3𝑥 + 7 cos𝑥)2 = 𝟐𝟖( 𝒄𝒐𝒔𝒙 + 𝒙 𝒔𝒊𝒏𝒙) + 𝟏𝟓(𝒙 𝒄𝒐𝒔𝒙 − 𝒔𝒊𝒏𝒙) + 𝟑𝟓 (𝟑𝒙 + 𝟕 𝒄𝒐𝒔𝒙)𝟐
Miscellaneous (Term 1 and Term 2)
Misc 1 (ii) Important
Misc 1 (iii)
Misc 1 (iv) Important
Misc 2
Misc 3 Important
Misc 4 Important
Misc 5
Misc 6 Important
Misc 7
Misc 8 Important
Misc 9 Important
Misc 10
Misc 11
Misc 12 Important
Misc 13
Misc 14 Important
Misc 15
Misc 16
Misc 17 Important
Misc 18 Important
Misc 19
Misc 20 Important
Misc 21
Misc 22 Important
Misc 23
Misc 24 Important
Misc 25
Misc 26 You are here
Misc 27 Important
Misc 28 Important
Misc 29 Important
Misc 30 Important
Miscellaneous (Term 1 and Term 2)
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