Example 32 - Chapter 5 Class 12 Continuity and Differentiability

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Example 32 Find 𝑑𝑦/𝑑𝑥 , if 𝑥 = 𝑎𝑡2, 𝑦 = 2𝑎𝑡 .Here 𝑑𝑦/𝑑𝑥 = (𝑑𝑦/𝑑𝑡)/(𝑑𝑥/𝑑𝑡) Calculating 𝒅𝒚/𝒅𝒕 𝑦 = 2𝑎𝑡" " 𝑑𝑦/𝑑𝑡 " " = 𝑑(2𝑎𝑡)/𝑑𝑡 𝑑𝑦/𝑑𝑡 = 2𝑎 . 𝑑(𝑡)/𝑑𝑡 𝑑𝑦/𝑑𝑡 = 𝟐𝒂 Calculating 𝒅𝒙/𝒅𝒕 𝑥=𝑎𝑡2 𝑑𝑥/𝑑𝑡 " " = 𝑑(𝑎𝑡2)/𝑑𝑡 𝑑𝑥/𝑑𝑡 " " = 𝑎 . 𝑑(𝑡2)/𝑑𝑡 " " 𝑑𝑥/𝑑𝑡 " " = 𝟐𝒂𝒕 Therefore 𝑑𝑦/𝑑𝑥 = (𝑑𝑦/𝑑𝑡)/(𝑑𝑥/𝑑𝑡) 𝑑𝑦/𝑑𝑥 = 2𝑎/2a𝑡 𝒅𝒚/𝒅𝒙 = 𝟏/𝒕

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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