Ex 5.4, 7 - Differentiate root e root x - Chapter 5 NCERT

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Ex 5.4, 7 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

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

Transcript

Ex 5.4, 7 Differentiate w.r.t. x in, โˆš(๐‘’^โˆš๐‘ฅ ), x > 0Let ๐‘ฆ = โˆš(๐‘’^โˆš๐‘ฅ ) Differentiating both sides ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ ๐‘ฆ^โ€ฒ = (โˆš(๐‘’^โˆš๐‘ฅ ))^โ€ฒ ๐‘ฆ^โ€ฒ = 1/(2 โˆš(๐‘’^โˆš๐‘ฅ )) ร— (๐‘’^โˆš๐‘ฅ )^โ€ฒ ๐‘ฆ^โ€ฒ = 1/(2 โˆš(๐‘’^โˆš๐‘ฅ )) ร— ๐‘’^โˆš๐‘ฅ . ร— (โˆš๐‘ฅ)^โ€ฒ ๐‘ฆ^โ€ฒ = 1/(2 โˆš(๐‘’^โˆš๐‘ฅ )) ร— ๐‘’^โˆš๐‘ฅ . ร— 1/(2โˆš๐‘ฅ) ๐‘ฆ^โ€ฒ = ๐‘’^โˆš๐‘ฅ/(4โˆš๐‘ฅ . โˆš(๐‘’^โˆš๐‘ฅ )) ๐‘ฆ^โ€ฒ = ๐’†^โˆš๐’™/(๐Ÿ’โˆš(๐’™ . ๐’†^โˆš๐’™ ))

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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.