Ex 5.3, 4 - Find dy/dx in, xy + y2 = tan x + y - Chapter 5 - Ex 5.3

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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise
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Ex 5.3, 4 Find ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ in, ๐‘ฅ๐‘ฆ + ๐‘ฆ2 = tanโก๐‘ฅ + ๐‘ฆ ๐‘ฅ๐‘ฆ + ๐‘ฆ2 = tanโก๐‘ฅ + ๐‘ฆ Differentiating both sides ๐‘ค.๐‘Ÿ.๐‘ก.๐‘ฅ ๐‘‘ ๐‘ฅ๐‘ฆ + ๐‘ฆ2๏ทฏ๏ทฎ๐‘‘๐‘ฅ๏ทฏ = ๐‘‘ tanโก๐‘ฅ + ๐‘ฆ ๏ทฏ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ๐‘‘ ๐‘ฅ๐‘ฆ๏ทฏ๏ทฎ๐‘‘๐‘ฅ๏ทฏ + ๐‘‘ ๐‘ฆ2๏ทฏ๏ทฎ๐‘‘๐‘ฅ๏ทฏ= ๐‘‘ (tanโก๐‘ฅ)๏ทฎ๐‘‘๐‘ฅ๏ทฏ + ๐‘‘ (๐‘ฆ)๏ทฎ๐‘‘๐‘ฅ๏ทฏ Using product rule in ๐‘ฅ๐‘ฆ๏ทฏ๏ทฎโ€ฒ๏ทฏ= ๐‘ฅ๏ทฎโ€ฒ๏ทฏ๐‘ฆ+ ๐‘ฆ๏ทฎโ€ฒ๏ทฏ๐‘ฅ ๐‘‘(๐‘ฅ)๏ทฎ๐‘‘๐‘ฅ๏ทฏ. ๐‘ฆ+ ๐‘‘(๐‘ฆ)๏ทฎ๐‘‘๐‘ฅ๏ทฏ.๐‘ฅ๏ทฏ + ๐‘‘ ๐‘ฆ2๏ทฏ๏ทฎ๐‘‘๐‘ฅ๏ทฏ= ๐‘‘ (tanโก๐‘ฅ)๏ทฎ๐‘‘๐‘ฅ๏ทฏ + ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ 1.๐‘ฆ + ๐‘ฅ. ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ + ๐‘‘ ๐‘ฆ2๏ทฏ ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ร— ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฆ๏ทฏ= sec2 + ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ๐‘ฆ + ๐‘ฅ. ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ + ๐‘‘ ๐‘ฆ2๏ทฏ ๏ทฎ๐‘‘๐‘ฆ๏ทฏ ร— ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ = sec2 ๐‘ฅ + ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ๐‘ฆ + ๐‘ฅ. ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ + ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏร— 2๐‘ฆ๏ทฎ2โˆ’1๏ทฏ = sec2 ๐‘ฅ + ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ๐‘ฆ + ๐‘ฅ. ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ + 2y . ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ =sec2 ๐‘ฅ + ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ ๐‘ฅ. ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ + 2y . ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ โˆ’ ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ =sec2 ๐‘ฅโˆ’๐‘ฆ ๐‘‘๐‘ฆ๏ทฎ๐‘‘๐‘ฅ๏ทฏ (๐‘ฅ+2๐‘ฆโˆ’1)=sec2 ๐‘ฅโˆ’๐‘ฆ ๐’…๐’š๏ทฎ๐’…๐’™๏ทฏ = ๐’”๐’†๐’„๐Ÿ ๐’™ โˆ’ ๐’š ๏ทฎ๐’™ + ๐Ÿ๐’š โˆ’ ๐Ÿ๏ทฏ

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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