Example 35 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Dec. 16, 2024 by Teachoo

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Example 35 Find 𝑑2𝑦/𝑑𝑥2 , if 𝑦 = 𝑥3+tan⁡𝑥. 𝑦 = 𝑥3+tan⁡𝑥 Differentiating 𝑤.𝑟.𝑡.𝑥 𝑑𝑦/𝑑𝑥 = (𝑑(𝑥^3+ tan⁡〖𝑥)〗)/𝑑𝑥 𝑑𝑦/𝑑𝑥 = (𝑑(𝑥^3))/𝑑𝑥 + (𝑑(tan⁡〖𝑥)〗)/𝑑𝑥 𝒅𝒚/𝒅𝒙 = 𝟑𝒙𝟐+𝒔𝒆𝒄𝟐 𝒙 Again Differentiating 𝑤.𝑟.𝑡.𝑥 (𝑑^2 𝑦)/〖𝑑𝑥〗^2 = (𝑑 (3𝑥2 +sec^2⁡𝑥))/𝑑𝑥 (𝑑^2 𝑦)/〖𝑑𝑥〗^2 = (𝑑 (3𝑥2))/𝑑𝑥 + (𝑑 (sec2 𝑥))/𝑑𝑥 (𝑑^2 𝑦)/〖𝑑𝑥〗^2 = 6𝑥+2 sec⁡𝑥 . (𝑑(sec⁡〖𝑥)〗)/𝑑𝑥 (𝑑^2 𝑦)/〖𝑑𝑥〗^2 = 6𝑥+2 sec⁡𝑥.sec⁡〖𝑥 tan⁡𝑥 〗〖𝒅𝒚〗^𝟐/〖𝒅𝒙〗^𝟐 = 𝟔𝒙+𝟐 〖𝒔𝒆𝒄〗^𝟐⁡𝒙 . 𝐭𝐚𝐧⁡𝒙

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Davneet Singh

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

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