Last updated at Sept. 6, 2021 by Teachoo
Transcript
Example 22 Find the derivative of (i) (x^5 − cosx)/sinx Let f(x) = (x^5 − cosx)/sinx Let u = x5 – cos x & v = sin x So, f(x) = (𝑢/𝑣) ∴ f’(x) = (𝑢/𝑣)^′ Using quotient rule f’(x) = (𝑢^′ 𝑣 −〖 𝑣〗^′ 𝑢)/𝑣^2 Finding u’ & v’ u = x5 – cos x u’ = 5. x5 – 1 – ( – sin x) = 5x4 + sin x v = sin x v’ = cos x Now, f’(x) = (𝑢^′ 𝑣 −〖 𝑣〗^′ 𝑢)/𝑣^2 Derivative of xn is nxn – 1 & Derivative of cos x = – sin x (Derivative of sin x = cos x) = ((5x4 + sin〖x) sin x −(cos x)(x5 − cos x) 〗)/sin2x = (5x4 sin〖x + sin 2x − cos x . x5 + cos2 x〗)/(sin2 x) = (−x5 cos〖x + 5x4 sinx + 𝐬𝐢𝐧𝟐 𝐱 + 𝐜𝐨𝐬𝟐 𝐱〗)/(sinx )2 = (−x5 cos〖x + 5x4 sinx + 𝟏〗)/(sinx )2 Thus, f’(x) = (−𝐱𝟓 𝐜𝐨𝐬〖𝐱 + 𝟓𝐱𝟒 𝐬𝐢𝐧𝒙 + 𝟏〗)/(𝐬𝐢𝐧𝐱 )𝟐 (Using sin2x + cos2x = 1)
Chapter 13 Class 11 Limits and Derivatives
Example 3 (i) Important
Ex 13.1, 6 Important
Ex 13.1,10 Important
Ex 13.1, 13
Ex 13.1, 16
Ex 13.1, 22 Important
Ex 13.1, 25 Important
Ex 13.1, 28 Important
Ex 13.1, 30 Important
Ex 13.1, 32 Important
Ex 13.2, 9 (i)
Ex 13.2, 11 (i)
Example 20 (i)
Example 21 (i)
Example 22 (i) You are here
Misc 1 (i)
Misc 6 Important
Misc 9 Important
Misc 24 Important
Misc 27 Important
Misc 28 Important
Misc 30 Important
Chapter 13 Class 11 Limits and Derivatives
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