Ex 5.4, 8 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at August 17, 2026 by

Ex 5.4, 8 - Ex 5.4

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Ex 5.4, 8 Differentiate w.r.t. x in, logโก(logโก๐‘ฅ), x > 1Let ๐‘ฆ = log โก(logโก๐‘ฅ) Differentiating both sides ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ ๐‘‘(๐‘ฆ)/๐‘‘๐‘ฅ = (๐‘‘(log โก(logโก๐‘ฅ)) )/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 1/logโก๐‘ฅ ร— ๐‘‘(logโก๐‘ฅ)/๐‘‘๐‘ฅ ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 1/logโก๐‘ฅ ร— 1/๐‘ฅ ๐’…๐’š/๐’…๐’™ = ๐Ÿ/(๐’™ ๐’๐’๐’ˆโก๐’™ ) (๐ด๐‘  ๐‘‘/๐‘‘๐‘ฅ (๐‘™๐‘œ๐‘”โก๐‘ฅ )= 1/๐‘ฅ) (๐ด๐‘  ๐‘‘/๐‘‘๐‘ฅ (๐‘™๐‘œ๐‘”โก๐‘ฅ )= 1/๐‘ฅ)

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