Example 22 (i) - Chapter 12 Class 11 Limits and Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
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)
Examples
Example 1 (ii)
Example 1 (iii)
Example 2 (i)
Example 2 (ii) Important
Example 2 (iii) Important
Example 2 (iv)
Example 2 (v)
Example 3 (i) Important
Example 3 (ii) Important
Example 4 (i)
Example 4 (ii) Important
Example 5
Example 6
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Example 8
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Example 11
Example 12
Example 13 Important
Example 14
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Example 16
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Example 18
Example 19 (i) Important
Example 19 (ii)
Example 20 (i)
Example 20 (ii) Important
Example 21 (i)
Example 21 (ii) Important
Example 22 (i) You are here
Example 22 (ii) Important
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo