Ex 5.7, 2 Class 12 Maths - Find second order derivative of x^20

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Ex 5.7, 2 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

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  1. Chapter 5 Class 12 Continuity and Differentiability (Term 1)
  2. Concept wise

Transcript

Ex 5.7, 2 Find the second order derivatives of the function ๐‘ฅ^20 Let y = ๐‘ฅ^20 Differentiating ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = (๐‘‘(๐‘ฅ^20))/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ใ€–20๐‘ฅใ€—^(20โˆ’1) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = ใ€–20๐‘ฅใ€—^19 Again Differentiating ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ ๐‘‘/๐‘‘๐‘ฅ (๐‘‘๐‘ฆ/๐‘‘๐‘ฅ) = (๐‘‘ (ใ€–20๐‘ฅใ€—^19))/๐‘‘๐‘ฅ (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 ) = (20 ๐‘‘(๐‘ฅ^19))/๐‘‘๐‘ฅ (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 ) = 20 ร— 19 ๐‘ฅ^(19โˆ’1) (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 ) = 20 ร— 19 ๐‘ฅ^18 (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 ) = 380 ๐‘ฅ^18 Thus, (๐’…^๐Ÿ ๐’š)/(๐’…๐’™^๐Ÿ ) = 380 ๐’™^๐Ÿ๐Ÿ–

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.